hi - welcome to the board.
first off, i'm glad you're planning to go see your doc. always a good idea. they are good at ruling out the really dreadful worries.
interesting that you experienced the gland issues. about the time my depression morphed into anxiety, i too experienced the same thing. soreness in the glands under the arm and in the neck as well as in the groin area. it eventually subsided, but hung around for months before it did. long enough to totally freak me out. be careful about checking them. they are very sensitive areas, so probing the glands to check them can cause them to become more tender. best to acknowledge that they are sore w/out actually touching the areas.
nothing you described in your post above falls outside what can be experienced w/ anxiety. and it sounds like you are pushing your academics quite hard, so it is likely that you are under a good deal of stress in that arena. you'll need to do your best to balance the stress. i can tell you w/ complete honesty that i am a physically healthy individual and have experienced every single symptom you described. every single one. the chest pains, the dizziness, the whole package. and it always flares up for me worse when i am under stress; be it work, family obligations, etc.
so do go to the doctor, my friend - rule out a physical problem. but in the meantime, try to counter your "what if" thinking. because it is very plausible that it is simply your mind generating the symptoms. the mind is so powerful. it can totally play games w/ you physically. i've dealt w/ anxiety for the better part of my 36 years on this planet and i've always been healthy as can be physically. but have often felt as though i must have tumors, cancer, and every other malady known to man. never pans out. i always check out physically well. the mind is INTENSE.
become an investigator of your symptoms, not a worrier over them. go get check out by the doc and if all is well, then you'll need to do your best to relax and put your mind on other thoughts.
i hope this helps even a bit and i hope that both your stress, and the symptoms you are feeling, are quickly alleviated.