I don’t see why not! I missed quite a lot of year 10 myself, dropped out of school for year 11 and started afresh with my GCSEs through self-studying, and I ended up with the equivalent of all A*s and As.
I think it’s doable, but also remember that whatever GCSE grades you get, when you get to the point of applying to Oxford you should explain in your Personal Statement how much time you had to miss due to extenuating circumstances.
Best of luck with everything!