It's a simple answer - that's not so simple to fix.
The feeling that you are choking is just anxiety, the anxiety is heightened because you are concentrating on the feeling, when our anxiety is heightened we stimulate our primal "fight" or "flight" mechanism, when we stimulate our primal "fight" or "flight" mechanism we usually suffer intensely (as in your case) because there is nothing to fight and no-where to run.
The solution then is to not get anxious when you go into class, because the anxiety is causing the feelings and if we remove the anxiety then you WILL remove the feelings - and "bingo" you're cured.
In reality it is not that easy, if it was there would be no-one on this site. But just understanding that it's your anxiety about throwing up helps because you can get a hint of where your anxiety is coming from - you don't want to embarrass yourself in front of everyone and this feeling you get is perhaps a physical manifestation of that concern?
Who knows? - that is just me having a stab at it from what you have wrote here, but it is definitely something that is no doubt causing you some anxiety and so it is the cause(s) of your anxiety that you need to work on, not the feeling of choking - the choking feeling is merely a symptom - I'm convinced of that.
So you need to reduce your anxieties somehow, explore where they are coming from and find out what they really are, so that they can be reduced. This can be done with professional help or by yourself with self-help. However if you need results quick because you are at the end of your tether then professional help is the way as self-help is a slower route. With self-help it takes longer to figure out what is wrong, takes longer for things to settle down and takes longer for everything to turn around again (not always, but usually).
It is absolutely fine if you can't handle that and know that you can't be patient enough to go down that route, everyone here understands that and if that is the case then you need go down the professional route instead .
Help and relief from a good professional can give far faster "results", but you have to be prepared to follow their advice to the letter, (IE: If they prescribe meds then you have to take them, etc.) it is no good seeking professional help and then taking their help half-heartedly you have to throw yourself into it and put your trust in their hands (so try to make sure your research is good and that you have got a good one) and not everyone can accept that. When we put our trust into someone else's hands and then don't see IMMEDIATE results - the professional starts to come under scrutiny, under question. "It's not working", "I'm not sure he's any good", "he's put me on medication I don't want to be on!!", etc. , etc. and when that happens we are in trouble because that will only develop more anxiety!!!
And the more anxious we get then the less effective the professions help becomes and so the questioning of the professional becomes a self-fulfilling prophecy!! This is the BIG trouble with anxiety - we fill ourselves with so much DOUBT and FEAR that we EVERYTHING comes under scrutiny, everything gets questioned and because of that nothing much gets given the chance to become effective and so when we SPOT that going on "AAARRRGGGHHHH!!!" we claim to ourselves, "nothing is working, am I doomed to be like this forever!!!
". and so the cycle is perpetuated.
So like I said: Simple answer - not so simple to fix
Hope it helped.