My advice is to go to an opthamologist ASAP. I have lazy eye. It was spotted when I was very young. baby? toddler? I don't really know at what age. But, at age three I had surgery to correct it. Although mine didn't wander on occassion, it was turning in. Apparently the younger you are for the surgery, the more successful it is. I have never had any problem with it since and I am 35 now so I think it's safe to say I never will. The vision in this eye is not as good as it is in the other eye, but still isn't bad enough for glasses. I did, however, wear glasses for several years after the operation. I suppose this was probably to help prevent it turning back in.
Also, there are two theories on this condition. An opthamoligist (surgeon) believe it is the result of the ouside eye muscles being stronger/ weaker (weaker in my case as the eye was turning in not out). So the treatment was to actually go in and cut the inside muscles to balance them out by wekening the stronger ones. An opthomologist (not a surgeon) believes that the brain just need to be convinced to use the eye and that altering the muscles to straighten the eye is a cosmetic surgery.
I am very glad my parents took the initiative to have the surgery because I have met people with lazy eye in my adult life and talking to them while one eye appears to be focussing on the ceiling really is rather odd... glad other people don;t experience that when talking to me.
When I was a teenager I went to an optomotrist, who suggested the there were eye exercises that could be done to strengthen the muscle further. BUT, that there was a risk that the brain would resist such treatment and respond by turning the eye back in. The optometrist felt there was nothing wrong with the eye physically and that it was more a case of my brain refusing to use it. I didn't want to take the chance of the eye turning in again so I never did the exercises.
I hope this helps. If I were in your shoes, I woul seek out an opthamoligist and an optometrist and see what they advise. I definitely would not stop at the GP or the optometrist. I think the opthemologist point of view is well worth exploring.
Also, I should add that my surgery was in 1973, so beliefs/practices in medicine may have evolved since then.
Good luck to you.