I never get THIS anxious about ordering meals, but I do suffer quite a bit of anxiety regarding going to new places and doing new things. Stuff like riding a busline I've never been on before (i.e: not knowing where the stops are) will seriously freak me out - likewise, attending a con I've never been to before and not knowing where to go to get my registration sorted out, etc.
I rarely get nauseous, but I do get stressed enough that I can't sleep properly and/or start crying at the slightest thing - and it is difficult to deal with, because it limits me and what I WANT to do, and that sucks.
I've been getting a little better at it lately, mostly by repeating to myself that people don't care about my mistakes as much as I do. They really don't. What seems like a huge and significant and scary thing to me is just a funny anecdote in theirs. That Subway you were at probably deals with dozens messed up orders every day, so yours probably won't even be remembered by the end of the week. The feeling that I've maybe made trouble for someone else is TERRIBLE - like, what if they hate me now? What if they go home and they complain to their family+friends about what a horrible person I've been? etc., etc. - and is probably a fear I will never quite get over, but realising that the staff of a restaurant (or whatever other place you're visiting) is there to help you will go a long way. Asking for help won't make them dislike you. That Subway-person sounding annoyed was in all likelihood NOT directed at you - but at some other customer.
And rest assured - as long as you are polite and don't raise your voice at people, you're going to be a significantly less annoying customer than a good number of people they deal with every day.