I would check the BA Terms and Conditions on their website first to see what the change fee will be. If it is a set amount ( like $150 per ticket) plus adjust to the current price, it may not be so bad. Ticket prices are usually lower for November travel.
Then call the travel insurance company and ask what the procedure is for making and supporting a claim for reimbursement. There may be "'pre-existing condition" rules that apply.
With that in mind, then call BA to change the ticket. Or do it online through Manage My Booking if you can, as wait times for phone calls are generally quite long. it have successfully changed BA tickets online several times but they were mileage tickets; it may be different for purchased ones.
While I have been successful in getting a flight date changed without charge for medical reasons in the past (2002), I would say that the chance of an agent waiving the change fee is virtually nil these days.
Good luck with your recovery! Everyone I know who has undergone that surgery has had excellent results and I wish the same for you.