I also have anxiety, so I relate to your experience. I don't have it so bad that I've ever thrown up from work-related stress and anxiety, but I've definitely gotten sick before. I think you have to consciously mitigate your thought processes. Firstly, it is not a big deal that your close wasn't good, as you are new to that store. There's a learning curve for a new store, for both the habits of the store and the people who work there (not everyone cares about or prioritizes the same things). Different stores have different features, different hours, and different numbers of customers too. Secondly, you have to let that shit go. Your manager is not going to give you constant reassurance. You need to take enough consolation in the confidence you have in your own abilities. The other thing about caring that much about people's feedback is people give stupid feedback sometimes. In workplaces, especially fast-paced ones like Starbucks, no news is good news. If you get no feedback, it means you're doing a good job. If you get negative feedback, it means someone felt like doing some "managing." If you care this much about your job performance, the chances that you're doing a poor job are slim. Keep working as hard as you do and you'll be fine. Starbucks is not an environment that punishes people for not being perfect.

I've been meaning to start a meditation routine. (I used to have one a long time ago but stopped.) It's good for anxiety, as it exercises the brain in letting thoughts happen and then pass without giving any energy to them.