Sometimes there are crooked teeth, sometimes the skull/bones are no symmetrical, and sometimes it is a mixture of both.The photos appear to show straight teeth but assymetrical bone (maxilla bone of the skull). Probably the most predictable solution is surgical, with orthodontics a likely follow up treatment. While the word surgery can seem daunting, it is a safe and successful procedure. Having said that, "there is no such thing as routine surgery."The right side needs to be lifted or elevated. Braces alone can be a challenge to do this, but with newer techniques using temporary dental implants as anchors, it MIGHT be possible.Gums follow bone, so if some bone on the right side was removed/elevated, the gums will follow. This will create much longer teeth, so they would need to be shortened. This will likely expose enough dentin to require crowns on the lifted side, possibly even some root canals if the teeth are shortened significantly.I would seek advice from an orthodontist that has experience working with a surgeon. This will increase the chance that ALL your options will be presented and discussed.