Alright, sorry for glossing over your previous statement about the state sponsored health clinic wanting to medicate you and then evacuate you. It makes sense that they would do so with their limited resources and the triage approach they must employ... They're simply not set up for the kind of counseling you seek. I hope you won't take it personal. Given your official reception, I think it's time to get creative. It's awesome you actually WANT therapy. It took a lot of us decades to get to that head space. So I want you to keep up the good fight and stick with it!
This may seem far-fetched but I was serious when I suggested that you engage with the psych department directly, either through administrative channels or through the PhD. students listed on a resource like this: Grad Student Profiles
Your message is compelling so just start sending it in emails. Yeah, you'll have to put yourself out there a little but healing is about courage and doing so conveys a level of sincereity and desire that is hard to ignore. Give them a sketch of the problem in breif terms and ask for suggestions. Briefly ID five things:
1. History of sexual abuse
2. Non-supportive family
3. Non-supportive mental health infrastructure
4. Anxiety about travel
5. Desperate need for counseling
Although there are a lot of hacks in the world, I think people start off in the helping professions because they really do want to help. You are a young person who wants that help and cannot find it. Certainly, someone at an institution of higher learning has the power to see that you get a little help -whatever it might be. And something is always better than nothing. Don't give up. Get creative.