It's possible to get an allergic reaction to suntanning, and also you could have a problem from tanning if you are on certain antibiotics. I hate to second the notion that you have already rejected, but it's kind of crazy to tan. Based on how my mother-in-law's arms looked, tanning a lot early in life gives you cooked-turkey looking skin later in life, and at 19 you look beautiful enough without the help of tanning. You need the help of undamaged skin more when you're 39 than you need tan skin at 19.
my sister and i had the same problem once before. we both tan for a couple months ever year i got it first and my doctor told me it could be like a heat rash and i most likely got it on my stomach b/c its a sensitive place. i also worked at a few salons before and the first one i worked at i got a rash on the back of my leg and a little on my back it was a chemical burn my boss didn't wipe all the cleaner off. but she put some kind of cream on it and it went a way in a few days. now my sister had a rash on her stomach and upper legs and hers was a reactions toward a new lotion and the heat but she only got a rash on the parts where she was more tender at she had to take steroids to make hers go away. but i do remember my doctor telling me how nasty tanning beds are and that you can catch so many things in them he said the best on to use is the stand up but even that on you need to wear flip flops or stand on a towel b/c you can get fungus on your feet.