Welcome! Sorry to read that you have been so unwell, but pleased that you have found LHC as a result. Really any concerns over hormonal birth control need to be addressed with a medical professional. As you are UK based, the nurse at your GP practice may be happy to have a chat.
Ill health has the same effect on the body as any stressful event, and shedding is unfortunately a common occurrence shortly afterwards. I don't wish to pry but is there nothing you can do to improve your diet, could you ask for a referral to a hospital dietician perhaps? Healthy hair needs a lot more than just vitamins - it also needs minerals, essential fats, protein and calories generally. These don't all have to be from fresh produce if this are not freely available; canned pulses, frozen vegetables and dried fruit are all very nutritious.