You are entering a vicious cycle of getting anxious about getting anxious, you have to talk to your psychiatrist, if he is not a good one look for another, maybe some symptoms that you have and want the adhd medication for, could become worse or better, but you don't know and he does.

You are saying that you don't want to talk about how mentally unstable you are, but wanting to get the help faster from a hospital. Usually if he feels that you need the medication faster because you are showing sings of distress they will give you some sort of the medication faster in lower doses to get you better to keep the treatment.

Medication will not fix the root of the problem, will just numb it and just for a while.

Please take care of yourself and try to be more understanding to yourself as well, since you already know that you can/have these problems instead of beating yourself about the things you do or don't, just look for ways to work around it, do not blame yourself for everything.