Is it your first OU course? They are actually quite flexible with deadlines in any case, so long as you have a legitimate reason, so I really don't think you will have any problems.
Don't give up yet!
Their student support are absolutely fantastic, why don't you give one of them a ring and chat it through with them.
I think you should be able to set out your issues pretty much how you have here and consider if there is anything else they can do to support you. They may ask for a doctor's note to confirm medical lessons.