Since you had trauma to your lips at a young age and now the lip is appearing bigger , so it can be due to hypertrophic scar formation. The various treatment options for such scars are chemical peel, dermabrasion, laser or resurfacing of scars, soft-tissue augmentation, intralesional steroid injection (keloids) and excisional surgery in selected cases. Please discuss these treatment options with your dermatologist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.