3 GCSE's but somehow in Sixth Form, what can I achieve with this?

I’d suggest redoing years 10-11 from scratch to bring your results up to date. Unis will definitely accept that bearing in mind your depression.

Of course they would accommodate for it. You can even reapply for oxbridge after Ye13 if you fail the application in Yr12. A boy in my class fell ill in Year 10 and redid that year and he’s currently in Year 12 even though his birthday suggests he should be a year above.

If you redo your GCSE’s any university will accept that 100%. Remember, you’re someone who’s battled depression. If I saw someone who had done that and managed to redo his GCSE’s and do well I’d be pretty amazed at how much they managed to turn around their life. That’s impressive stuff tbh

Oh, and on a side note I noticed you said being homeschooled was a mistake. Was the fact you were not in a school environment affecting your motivation? If you find a good exam centre then the school will definitely allow you to come in whenever to talk to teachers about how everything's going. But I'd try to get at least an exam centre who will enter you sorted by the end of this month because it's pretty late into the GCSE year. Otherwise just enter as year 10 if you definitely feel there's too much workload you have to do. The following exams are recommended to enter as they're core and important subjects:

Maths
Triple science - Biology / Physics / Chemistry (foundation if you want, but do higher as top grades aren't available in foundation) This counts as 3 separate GCSE's.
English Literature and/or English Language (the latter is easier and quicker to prepare for)

Obviously this isn't many and you ideally want more. This is the best GCSE's to do on top of the above. It's a core subject and it's not hard.
RE

Then you can feel free to choose a few others if you feel you have the ability to do so. 8-10 GCSE's is a good amount, and the typical number is 11. But doing the above is fine. Choose what you can handle. Here's a few examples of what you might consider too.

Spanish / French / German / other language
Geography / History
Further Maths
Computer science
DT / Art
Business studies

Don't bother with languages, because you have to be able to speak it near fluently under the new spec unfortunately. Unless of course you feel you know some already, or you're fluent in it (got a language you speak fluently? do the GCSE for it).