Help - unsure about college

A bit of backstory: I fell very ill during my gcse's a few years ago and despite spending 6 months in hospital i came out ok. Mostly B's with a few A's but importantly a C in core science and A* in additional. Initially i had a lot of trouble getting into a sixth form because i wanted to study the sciences and of course they wouldn't accept a C in core science, dispite my explanations that i was ill and had very little ability at the time, using my additional grade as proof that i could achieve. After finally getting a college to let me study there i fell ill again - turns out i never fully recovered and pushed myself too far too quickly. So i ended up missing so much time they essentially kicked me out. i am now 18 years old and supposed to start a applied medical science btech next week. But i am now really unsure on what i need to do to get into uni on the course i want.

To start i'm going to state my endgame: I want to go to university and study Biochemistry. Although as we both know the last two years have not been to helpful for me. I am currently signed up to do a Level 3 Btech in Applied Medical Science at City of Bristol, when i initially went there they said they would let me run a chemistry A Level alongside the course (given the course is only 2 days a week) and help me as much as they could to achieve a decent grade. Upon enrolling however they seemed to have changed their minds and will not let me sit it with them, even if they did consider it i think i would of had an issue with my core science grade but i'm trying to take things one step at at time.

Mother is very insistent that i take another year out and then apply for an access to higher education course, but i've been given the all clear health wise and don't want to sit on my ass for another year.

Btech requirements for universities i want to apply for such as Bristol require DDD with a chemistry or other science A Level. And personally i really enjoy chemistry, i will admit that i may not be the quickest learner but overall it was probably my favourite thing about the last two years. And given the opportunity to even just do the one A Level elsewhere and apply for a foundation degree i would probably jump ships.

Just wondering what your take on all this is and if you could possibly offer some advise.