Firstly, I want to wish you the best of luck in this!
I'm just wondering if there's a sixth form or college that you can enroll in that will help you through this process?
I think that IGCSEs will be a walk in the park once you've done A levels, so maybe take them in the same exam series (I don't know if this is possible, but you'll be almost guaranteed good IGCSE grades in maths and science).
I'm currently studying biology, chemistry and maths at A2 so I can give you a bit of insight into the difficulty of the course. I have only ever self-taught biology AS- I did it over 5 weeks whilst also preparing for some aptitude tests and being abroad for a bit. I'm fairly confident that self-teaching biology will probably not be an issue. Whilst AS maths is fairly simple for anyone confident in maths, A2 maths is not a walk in the park- however, I do think it's possible to self-teach it. Don't forget that you can only do well in maths if you do a huge amount of practice- you will need to leave time for a lot of practice after you've actually finished learning. For me, chemistry is the issue. Chemistry A2 gets extremely difficult, and there is a huge amount of information to learn. I personally wouldn't be able to do it in a few months.
If you really want this, it is most definitely possible, but it may take longer than you expect. Please let me know if you want any more insight into these A levels or my experience with self-teaching biology.