It's a bit of an odd position that you're in as you're between education providers. It would usually be free because you're under 19 but with you not strictly currently being in education they can be fussy.
All you can do is contact your dentist and see what they say.
Once you're at uni, join the local uni dentist and apply for the HC2 certificate as early as possible. Some people get them, some don't but if you are given one they are an absolute lifesaver. Mine didn't ask about parental income so it was granted fairly easily.
Good luck with your poor teeth!