WARNING: I am NOT a doctor.
Greetings ehsen,
Tightness in the neck and shoulders may be from stress, improper breathing, improper body mechanics, driving with the head/chin forward, watching tv/computer with the head/chin forward, poor posture, and lots of other reasons we haven't yet discovered. Intense push-ups will develop your pectoralis, biceps/triceps (depends on the angle of the elbows). If you are not balancing your muscles then the bones will move to the stronger muscles. I am guessing that you have rounded shoulders. Look at your posture. Which direction are your shoulders? I am guessing that your shoulders are forward toward your chest. When people work one muscle group without working the opposite muscle group you will have an imbalance. You will need to stretch your pecs (doorway stretch) and also do exercises for your back.
There's a book called Relaxercise that may help your condition.
See a reputable massage therapist.
Make an appointment with a physical therapist, chiropractor, or osteopath doctor.
If any of the following advice gives you a sharp pain....STOP!
In the mean time try to relax. Take a deep breath. Where does the body move? Do you notice movement in your chest, shoulder, stomach, or back? Your breathing should be abdominal (your belly). How does it feel when you slowly push your shoulders down and hold for 10 seconds? How does it feel when you slowly lift your shoulders up to your ears then back so you can squeeze your shoulder blades together and hold for 10 seconds? When you gently rub under your collar bone (from your arm to your sternum) can you feel the tightness of the muscles? Make a fist and gently rub your sternum back and forth (this will be uncomfortable). You will need to stretch your chest.
Here are two clips about the Alexander Technique that may help. Disregard the mentions of picking up girls at bars.
Alexander Technique Part 1
http://youtube.com/watch?v=wwET_AVjiuU&mode=related&search=
Alexander Technique Part 2
http://youtube.com/watch?v=wTTXWPG4Rjw&mode=related&search=
The body needs to learn what it feels like to relax.
Next time you jump rope look in the mirror. How is your body mechanics? Do you warm up and stretch? Also cool down and stretch? Drink plenty of water? When you use the bathroom your urine should be clear. If it's yellow then you need to drink more water (or else you are taking vitamins).
Do you notice when your shoulder goes up? When your head/chin juts forward? Next time you drive, watch tv, on the computer, when you walk, attempt to notice your body mechanics.
Pain killers only hide the symptoms and does not go to the source of the problem. I highly suggest you see a medical professional. I am NOT a doctor.
Hopefully you found this info helpful for your situation.