So we hurt ourselves when we train and when we spar. And then our supporting wives, meaning mine has to tell us to stop cowboying up & go to the chiropractor.
Your wife must be a lot nicer than I am! I tend to tell my husband that if it hurts enough to groan and complain about, then go to the chiropractor. He doesn't cowboy up in silence, instead he is very...verbal about his discomfort

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Seriously though, several years ago I used to be a licensed massage therapist and worked with several athletes. Their coaches would usually have them soak in the coldest bath they could stand after a hard training session, in an attempt to provide cold therapy to any slight injuries that they might have sustained during the session. You can also do this for specific areas, if you have worked them hard. For example, if you have done lots of blocks during a particular session, you might think about going home, filling the kitchen sink with cold water and some ice, and soaking your forearms for 10 - 15 minutes, take a short break, and then soak again. Even if you don't have any symptoms at that time. Feet, hands, and forearms are easy - it gets tricky to spot soak the rest of your body unless you soak all of you in a bathtub. You can always take a short cut and just apply an ice pack to the overworked areas.
BTW, some cheap and effective ice packs can be easily made by combining isopropyl alcohol (aka rubbing alcohol) and water in a 1:1 ratio in a zip-lock, water tight plastic baggie and storing it in your freezer. The combined liquids have a low freezing point and will not freeze hard in most freezers, so will contour easily to hips, legs, elbows, etc. I usually double up with two bags to keep any leaks from causing a problem. Also, when using this or any ice pack, be sure to use a protective layer to keep your skin from becoming damaged from the excessive cold. I like using a piece of cotton flannel fabric, but cotton gauze or any thin fabric layer will work well.
When I wake up the next day with a previously undetected injury, I usually apply arnica gel if it is a bruise or Tiger Balm or other topical analgesic if it is more of an ache or tight muscle. For swollen areas, I use the RICE formula - rest, ice, compression, and elevation. My most frequent area to come up with these irritating "creepers" is my knees. I suspect I have slight arthritis in them already. If we do lots of kicking in class or lots of hard, quick, lateral directional changes, I usually wake up hurting the next day. So far I have had good results with the analgesic ointments plus deep tissue massage of the quads, and wrapping the affected knee with an elastic bandage to remind me to baby it for the next day or two.