I'm a physical therapist student, i might be able to help but you should really go see a PT as there are so many things it could possibly be. If there is pain and what looks like inflammation around the inside of your elbow (red, swollen, warmer to touch) then it could very well be golfer's elbow. When you flex your wrist actively or against some resistance (palm of hand towards forearm) is there pain in elbow? Is there pain when you passively (use your other hand to bend back) extend your wrist backwards? If not, then it's not golfer's elbow.
The arm band idea, don't do it, unless a therapist prescribes something, most of those OTC braces are there for just mental security. It could be a ligament problem. If it seems to be, from what I told you about golfer's elbow, light weight eccentric wrist exercises a few times a day for a couple weeks should nip it in the butt, along with cross friction massage, icing, stretching.
Hope that helped!