I was wondering how long I have until it's too late for me to apply for exam retakes
You can in theory be entered right up to the exam though not every centre will do late entires and the price would be high. The official deadline for normal entries is in February next year but if you are trying to resit units from A levels that have been reformed you may find it harder than usual to find a centre that is offering them. Make up your mind about what you want to do and get it organised as soon as you can. Try your old school first as they may be willing to help even if they don't normally take private candidates.