Generally speaking, they do not "lock you up" against your wishes unless:
You are a harm to yourself.
A harm to others,
Unable to care for yourself.
Community mental health systems vary from one location to another, so it's difficult to guess as to just what they will do for you re: hooking you up with a sooner appointment, etc. I am guessing they will help you as much as possible.
have you called the pdoc you will be seeing to let him/her know you need to see her/him sooner? You can also ask to be put on a cancellation list.
Please do go to the ER if you need immediate help.
Take good care of yourself.

WC