If your orthodontist told you that surgery was needed, I'm sure its accurate. In an adult, you cannot successfully widen the upper jaw without surgery or you are likely to cause gum tissue and bone problems.
With that said, it is possible to accept a compromise in your result and simply line up the teeth without surgery and leave your upper jaw narrow. Thus, your bite will NOT be corrected. While this is not the favored and best option, it is still an option. From my perspective, why would I make someone live their whole life with crooked teeth just because they didn't want surgery. Educate yourself, I'm sure surgery is the BEST option, but then discuss compromises.