Can I get into Cambridge with retakes and post A-level application?

I would love to apply for Cambridge medicine, but realistically I know I have no chance applying this year with my AS-level results. My stats for unreformed subjects are:
Maths- 90, 100, 73
Latin- 80, 78
I'm planning on retaking the two maths modules and both of the latin papers (I'm not quite sure what kind of UMS I need in Latin for medicine- or if it's even worth resitting at all) and I'm hoping to increase my UMS to 95+ for both subjects and get A*s in both biology and chemistry and apply post A-level.
I know I'll be retaking a lot of papers, but it has been difficult for me this year- a close family member passed away in February and I also ended up missing 2 weeks of school because of it and the situation at home wasn't too good either. My school is aware of why I missed school, but not about my home life. Would it be possible to mention these situations as extenuating circumstances? Is it even worth for me to consider applying?
I also come from a very good school. Will this put me at even more of a disadvantage when taken into consideration?

Sorry for the long message and thank you for taking the time to read it