Do not have surgery to fix an overbite. Overbites can be easily treated with orthodontics. Why your orthodontist did not take care of it is beyond me but I would confront him with that question. However, I have a feeling you may not be using the correct dental terminology in describing your problem. If you cannot communicate properly then the wrong advice may be given to you. First of all, many people use the term "overbite" incorrectly. An OVERBITE is a vertical problem and is the amount of overlap of the upper front teeth over the bottom front teeth. In an overbite case, when you look at the front teeth when they are together, the top teeth will cover up (overlap) the bottom front teeth. Since you stated that your teeth "stick out" I think you really mean you have an OVERJET. This is a horizontal problem (front to back direction) and refers to the distance the upper front teeth are ahead of the lower front teeth. When you look at someone with an overjet problem, the upper front teeth will look like they are too far away from the lower front teeth. Therefore, since you seem to feel that your teeth stick out too much, I will assume you are really talking about an OVERJET and not an overbite.
Assuming you really mean OVERJET it is easy to explain why your problem was not corrected. The reason is traditional orthodontists do not know how to correct overjets because they do not have the knowledge to do it. Functional orthodontists, on the other hand, do this type of correction routinely using functional appliances. In your case, since you already had braces (and hopefully did not have bicuspids extracted), wearing a functional appliance for 9-12 months or less should eliminate your overjet. Braces may or may not be needed depending on what things look like after the correction but it should be minor.