Anytime chest pain or pressure comes on while exercising you should stop the exercising and see a cardiologist. You always want to rule out other causes and not assume that anything is anxiety related. If getting this checked out merely eases your mind, it's well worth it! Take care!
I am also 18 and heading off to college (in less than a week) and I have been freaking out with anxiety at random times. Although it is pretty safe to assume this is anxiety your feeling...I would talk to your doctor just in case. If you assume it is anxiety and leave it un-checked, you dont want to end up getting really sick or hurt. If tests come back normal and the doctors say it is anxiety, then you can take the further steps to treat it. Medication combined with therapy is proven to be the best treatment, however there are a ton of alternative treatments if medication isnt your thing. Id recommend therapy to anybody though...everyone needs someone to talk to and that kind of guidance and such.
So, dont worry about it, but get it checked just in-case for ease of mind and so you can take the next steps to treat it if it is anxiety.
Anyway, excersize is proven to help anxiety. So is healthy eating. Chamomile tea helps ease anxiety, meditation, deep breathing (like, close your eye and lay down, breathe in slowly as much air as you can, hold it for like 3 seconds, then slowly let it all out...do that 3 times or more...whatever you want).
Those are just a couple techniques...Good luck, and youve taken the right steps posting on here...everyone pretty much is very friendly and trying to help.