Hey,
I've been where you've been. Well, sort of. I've had severe anxiety all through college, and it managed to manifest itself in all kinds of forms. It can be incredibly stressful and discouraging, but just try to keep at it! It'll be worth it in the end.
I'm not sure what causes your anxiety, but if you can address that problem it will go a long way. What worked for me was letting a close friend in on the situation; tell them the full story, and have them be someone you can be near and talk to when you're having symptoms. If s/he can be there and help calm you in class, that might help.
As well, and this go for any type of anxiety, you should get on a regular sleep schedule (hard in college, I know), eat regularly (nibble on snacks as much as you can, always have something in your belly), drink plenty of water (I've found dehydration, even in mild forms, makes the mind more susceptible to anxiety), and avoid stimulants such as caffeine as much as possible.
For settling your stomach, you might want to try ginger ale (sugary, but if it helps, it's worth it), or maybe even antacids like Gaviscon.
Hope that helps... I'm in my last year of college now (4th year) and still have anxiety symptoms (my panic attacks make me gag... sucky!) though managing them has become easier over the years. Hopefully it will get easier for you too. Best of luck.
PS: And as Patricia wrote before me, CBT is the best treatment for something like this; I did it years ago, and what I learned helps me still today.