A lot of universities will limit your number of sessions so that may be why they will refer you out if you have something a little more serious or something that may take a little more time to work through. I think my university limited it to 10 or 12 sessions per school year which is only about 3 months if you go every week.

I tried my university's counseling center during undergrad but I only went three times. I think it was more that I just didn't connect with the therapist than anything else. I'm in grad school now at a different university and I considered going to the university for counseling. However, I wanted the option to go long term if I wanted/needed so instead I found an affordable T who works in a local community practice. I've been seeing her now for 6 months so for me, I think it was a good choice.

I say give it a try though! If they decide to refer you out, they've done the work for you of finding someone who can help you out.