You can't give up.

Are you saying that you didn't tell them the "whole story", so they gave you contrary advice, and now you are confused because they didn't give you the advice you expected?

If they do understand everything I wonder if they have a predjudice against psychiatric treatment. If you feel suicidal, and they say not to go to the hospital, are they going to offer an alternative to not only keep you alive, but to have you working toward feeling better and able to deal with school/friends/life again?

I guess it is true that one shouldn't use the hospital to run away from ones problems. But you are not having a "difficult time". You have periods where you feel suicidal. You are unable to cope with the stress of school. It is keeping you from thinking clearly and from functioning day to day. It doesn't matter if you happen to feel good right now, what is the trend? Today you feel better, tomorrow will you feel hopeless again? Feeling suicidal even if it is only occasionally is NOT "ok".

You are not running from your problems, you are walking up to face them. Pretending nothing is wrong and trying to "work it out on your own" is running IMO, based on how bad you have been feeling recently.

It is like having all the symptoms of appendicitis but saying "Well lets just try to put an ice pack on it for a few days and see if it gets better before we 'run' to the doctor". Note I didn't say "Before you have surgery". I'm not suggesting you have surgery, I'm suggesting you go to the doctor and see if he thinks you need surgery. Reschedule and talk to the doctor. Waiting around to see if the appendix bursts is no solution, because then it is too late.