That sounds pretty tough then, especially with the uni's counsellor costing money...I do recommend trying to discuss your mental health with possibly your personal tutor?, do mention on the uni's counsellor costing money and you're not sure how to reach held elsewhere. You can bring it to them as an email, I occasionally schedule mine if I'm too anxious to see their replies right in the moment, or you can bring it in as a note.
Example of what you could write to them: Hello, I've been struggling with feeling anxious and unfortunately this is only getting worse overtime, I'm not sure what to do as I'm unable to afford the uni's counsellor. I'm afraid this may further disrupt my university work too and health. I would appreciate for any help with this.
You can discuss this instead with your teachers if you like as I'm unsure how directly involved the personal tutor is with its students so it's perfectly fine if you prefer to tell your teachers.
Bring a note if you decide to wait to come back home to do it at your home GP, where you explain all struggles, how it interferes with your schoolwork possibly and how it may be getting worse. However you're clearly concerned with your mental state now and I think it's best to act before anything could trigger it to make it worse so might be better to discuss with teachers. Hope you get this sorted, wish the best for you!