Ngl it will be hard. There are multiple factors to a medicine application: GCSEs, AS/A levels, how many repeats you're doing, UKCAT/BMAT scores, personal statement, work experience, interview performance etc. Usually you can compensate by making the other factors stellar if one of these is weak. Problem is GCSEs are the very first of these. So you'll be putting yourself under immense pressure to do well in the other things. That's as well as you need A*/As in all 6 GCSEs.
And also, you'll be closing yourself to many unis which strongly consider GCSEs so your choices will be reduced. You will have to choose your unis very carefully when the time comes.
Saying that, it's not impossible. And of course, keep a doctors letter and a letter from your school about your mitigating circumstances. That will help too.
Just one question, if you can't cope with more than 6 GCSEs, will you be fit to do 3 A levels? Because there is a LOT of work at a level, it is a huge step up. And not only do you need to do three hard a levels (chem and bio, many choose maths and physics as a third) you have to do well in them. At least As in all. All this comes with a good reason too, med school and the life of a doctor is very demanding. This is their way of testing if you're cut out for a life like that. Do you think you'll be ok to pull that off?