Hi Bobbyfly - the problem with heterophoria (eso or exo) is that when tired there's a possibility of losing fusion, leading to double vision.
I have no idea whether it's correctable through surgery, which is usually only done on adults for cosmetic reasons (and hence pointless for a phoria).
Your best bet at this point is to try to gain an appointment with a consultant ophthalmologist (your GP can set it up though there's a waiting list, obviously) and get a professional opinion over whether it can be corrected. You then need to send that off to the CAA and await their response.
Good luck!