Hey. I suggest you return to the college counseling center and request to see the Director of Intake, or Intake Coordinator, or Director of Counseling or the Director of the Center (depending on the levels). You will have to make an appointment.

Explain your situation to the person at the front desk and they will direct you to the appropriate person.

You need treatment and most college counseling centers will provide treatment. Some have rules like 20 sessions or 30 sessions, but you are ENTITLED to counseling because you pay the student fees (which cover things like this).

Now, obviously the therapist you saw was confused and should not have "discharged" you. Do not give up.
And make sure you tell the person you next meet with exactly your symptoms ~ SI, suicidal thoughts, etc.

Good luck.