I'm going to tackle the mental health stuff first. If those urges towards self-harm are, or at any point get to be, intense enough that you feel you would actually hurt yourself, then you'll need to bypass the counselor and go to an emergency service.
It's great that you've taken the step of making an appointment with a counselor, because that's going to help you get some supports that it sounds like will be beneficial to you. You mention being nervous about your first appointment. Is there something in particular that you're anxious about? If you haven't already read it, this piece may help you get a sense of what to expect from your appointment: Process This: Getting the Most Out of Therapy
As far as drinking goes, I agree with potatochipeater that there are plenty of other folks on campus who don't, or can't, drink. But, I can definitely see how you'd feel like you're the odd one out, especially if a lot of the social situations you're in involve everyone but you drinking. It sounds like you're enjoying the parties (although I would check-in with your friends about why they keep ditching you to walk home alone, because that's not a great move on their part), so it sounds like a next step would be to find one or two non-party activities to add to the mix that get you out and about and meeting people. That gives you a chance to meet new friends, as well as meet people who are potential partners. Are there activities or groups on campus that you've been thinking about joining?