Strabismus surgery is a common surgery in America. Taking this surgery only need half an hour in operation room. But about the recovery time it is different due to different age. Usually it need 6 weeks to 3 months, for the younger, the recovery time is faster. Other reason affect the recovery time is the surgery extension, the more extensive the surgery is, the longer recovery time.
Well, I can learn from your words that you are still not sure it your decision is right. As you know, strabismus is not a deadly disease but it should not be ignored, since it could affect your life and eye health. So, if you are going to the right place, and if everything goes right, it will take about three months before it recovers. Also remember, the final say goes to the doctor.
Usually, people with strabismus surgery can expected their eyes be in a good position after the surgery. But it said that you shouldn't expected it will change too much. And the eyes will slightly with healing over 2-3 weeks. Anyway, you'd better ask your doctor how long it will spend for you to recovery.