Yeah at this point you would not be eligible for Starbucks insurance until open enrollment again in August. There are no QLEs that would qualify you at this point.
If you absolutely *need* to see a doctor, you can try an urgent care or a walk-in clinic. There may be a free clinic close to you that you can go to, I would recommend using
$1 to see what shows up near your zip.
Regarding identity stuff, typically the stuff they look for is like a state ID/Drivers License, passport, social security card, birth certificate, etc. so you should have that on hand for stuff like this. I'm going to assume you are pretty young (somewhere between 18-23, am I right?) so if you can, try to get ahold of that stuff *now* so you'll have it for the future.
You should also try Medicaid, and if you are under 18 I think your parents can even look into CHIP. Are your parents not able to walk you through some of this stuff?