Completely skipped Y10. Are my chances low for 6th form/Oxbridge?

Background:

• Moved to a new area about a year ago during Y9 summer (about to enter Y10).
• The local council was originally going to assign me to a certain school.
• But the headmaster of that school did not allow me to enter school for all of Y10, due to mental health reasons at my previous school.

During the past year:

• I got a risk assessment from CAMHS stating that my mental state has improved and I am now fit for school.
• The council hired an English tutor to help me with Eng Lit/Lang (who had years of experience at a boarding school).
• I've tried to catch up with the Y10 syllabus, but can only catch up with the main subjects (Eng Lit/Lang, Maths, Triple Sci). For the optional subjects, I might not have enough time to study them satisfactorily in Y11.

My question is: if I only study the main subjects for GCSE, would this severely limit my chances at a sixth form (or Oxbridge), even if I get all 9s in those main subjects and with possible extenuating circumstances (that my school didn't permit me entry for Y10)? Or should I just repeat Y10 (and would repeating make me less competitive for Oxbridge)?

Thank you for taking your time to reading this. Feel free to just ignore this post if you'd rather that. Also sorry if this post breaks any r/GCSE rules (I will probably delete this post if that happens). :]

Also I know there is a similar post on r/6thForm but the poster was asking whether to resit Y12. I am curious if the situation is the same for Y10 (since the majority of replies in that Y12 post recommended resitting).