Hi,
In short, yes. There are many arts which will give you a good range of options for grappling an opponent in order to control them, including the various forms of Jujutsu, Judo, BJJ, Ninjutsu and Ninjutsu-related schools, MMA schools, Wrestling schools, Shootfighting, Submission Wrestling, Hapkido, Aikido, Chinese art which teach Chin-Na, and many others. In fact, you will find that, other than the competition-based groups (Judo, BJJ, MMA, Wrestling etc), the emphasis will be on a smaller person controlling a larger, so it should be even easier for you to apply the skills.
There is a "but", however. Grappling skills typically take longer to develop than striking, as the technical side is a little more involved. So if you are after something that you can learn quickly and easily, that may be a bit harder to find, and will come down to individual instructors rather than systems.
As for your want to concealed carry a firearm, but not want to shoot, you know, this may be the non-American in me, but for crying out loud, guys, you don't want to shoot someone, don't carry a gun! Really, don't!
Okay, that's out of the way. If you are going to carry a gun, then you probably need to recognise that the two concepts you are talking about here go against each other. To grapple and control an opponent, you need to be close to them. Very close. And if they find your weapon, then it will be within their reach, and you may find yourself facing down the barrel of your own gun. On the other hand, to employ a firearm, you will require space (to draw the weapon in the first place, aim it, keeping it away from your body, and be far enough away that your opponent cannot reach out and attempt to take it from you). So you will need to make a decision quite quickly each time, are you going to go in and control, or are you going to stay back and draw your weapon. As a police officer, this question would come up a fair bit, but remember that they are going to have procedures and policies in place to help make that decision for them, as well as the fact that they are expected and required to engage, you as a public citizen are not.
As for your encounter, which appears to have prompted this train of thought, you give a number of reasons that you didn't fight.
I refused to fight (because):
A)I did not want to get into a fist fight because I KNOW I would get hit even in delivering my own blows
B) I had little knowledge of how much he knew how to fight
C)Risk of arrest
D)Lack of knowledge of what he had in his own possesion
E)Fear of escalation[my father was there and was in possesion of a small pocket pistol that he always carries and if this kid pulled a knife or worse, he was a gonner]
I would ask if these were reasons at the time, or justifications you came up with later. The reason I say that is that in a real encounter your adrelanine kicks into high gear, and that reduces your higher brain functions, such as complex thought. Many people mistake this as fear, but it is really just the effects of the adrenaline. So if that is the case, your actual reasons for not engaging will be a bit different. Not saying it is a good or bad thing, just that you either weren't in a situation that you considered bad enough to kick off your adrenaline to any great degree, or that you would not have been able to think about things such as "how much he knew about how to fight".
We'll go through each, though, and through that we'll hopefully lead to place where your real answers will be revealed (by that I mean the answers to the question you're not actually asking).
A) Yes, in any physical encounter there is the very real probablility that you will be hit, and hit hard. And, obviously, the longer you are in a physical altercation the greater the chances of you recieving damage. But if this is what stops you getting into a fight, then it will always stop you. I feel this is more the mis-interpretation of adrenaline as fear, which, as I said, is pretty common. But do get an understanding of verbal de-fusing and de-escalation tactics, as they can help avoid the physical side of things and therefore avoid the danger of being hit.
B) While I appreciate and agree with the Sun Tzu quote in your signature, remember that it is based on two opposing armies fighting each other, where information gathering can give you a pretty good idea of the disposition of the enemy forces (how many are there, how much in the way of archers, or cavelry, what their supplies are like, if they have re-inforcements available, who are their allies, who are their enemies etc), and that simply isn't something you have the time to do with the drunk guy in the bar getting abusive. There is some basic stuff you can do (how they shape up may give you a clue as to if they are a grappler, striker, or kicker, whether they have a weapon etc), but generally you will never really "know" what you are facing until you are facing it. Again, this comes across as thinking about the situation later, and asking yourself "why didn't I?', and coming up with this and other answers in order to convince yourself that you didn't "chicken out" (for the record, I don't think you did, just maybe mis-read yourself and the other guy. But we'll get to him).
C) Risk of arrest. See the answer to A. And if there are a number of Police Officers in your family, then you should be able to get advice fairly easily on how to handle such a situation.
D) Okay, in the US, particularly in the South, it is a very real possibility that anyone you get into a fight with may be carrying a weapon of some kind, even up to a handgun, so this is a very cogent point. One of our instructors went to the US a while ago for business, and when he came back said that everyone was so polite... mainly because everyone seemed scared of who may or may not have a gun! That is not a good thing, by the way...
But you counter this with your next reason, giving me the impression that again, this is an after-thought type reasoning.
E) Here you do know what weaponry is on "your" side, and you are concerned about the application of the same. Again, if you don't want a gun to be used, don't carry the damn things! But really, this is you saying that if things escalated, they would be out of your control. And if things got out of hand, you would feel responsible. That is a little unreasonable, really. Your argument here is that if the other guy pulls a weapon (his decision, out of your sphere of control), then your dad may pull his gun (his decision, out of your sphere of control), and you would feel responsible. So you don't start anything because you cannot predict the end. Again, I refer you to the answer to A for this aspect.
But there is an important part of this story you've missed. Why didn't the other guy escalate? What stopped him? In this we get our answer to what you are wanting.
He didn't escalate because it would nave been absolutely suicidal. He was fine following a few girls and intimidating them, but then when faced with yourself and your father, he didn't continue. He was most likely challenging you in order to try to salvage self-respect, or possibly to gain/maintain an Alpha position over yourself (designed to impress the girls, but not done in a good way. There are much better, and much more effective ways of doing the same thing). If you had said "yes", he most likely would have backed down.
Going through your profile, there is no mention of your age, however you mention the other guy as a "kid" at 18, your occupation is listed as "student", and you intend to conceal-carry "when you are of age". Not knowing the exact laws of Florida when it comes to firearms, I will assume you are about 20? You also decribe yourself as quite big (I am reading that as fairly solid, well-muscled, as opposed to simply "heavy"). So you are already quite an imposing figure, yes? However, despite this physical advantage, you are feeling a little less-than prepared should something come to a physical head. From your profile, it appears you have already looked into various avenues to fill this void, and they haven't quite worked out for you yet. And a few of those are exactly what would be recommended if we just take your post on face value (Aikido, Jujutsu, Judo, MMA).
So what are we actually asking here? Well, the general question I get out of all of this is this: "How do I control a situation so that there is the minimum of risk to myself, and the minimum of risk of escalation or danger to the opponent?" Well, that is something you will need to find within yourself. But an instructor (if they're good) can help you find it. Look again to the arts mentioned, but look closer at the instructors teaching. The biggest things you will need are confidence (which comes with experience), and time to learn. These skills will not come overnight. And do not neglect the de-escalation side of things. If you can, do a security-trainer course. It should be almost nothing but restraint and removal techniques, but won't give you the depth of a complete system.
Hope this helps, anything else just ask.