I've noticed recently that my hip seems to be a bit shifted to the right. Should I be concerned? If so, what would be the best way to fix it?

Weight control. I am sorry for your condition but you can at least control your weight -- the lighter you are the less strain to the back and legs.
Varies . A "shift"!of the hip can be caused by problems at the level of the hip, pelvis, or spine. If it is causing you concern, I would not hesitate to be seen for a specific diagnosis.
Let me try to unders. How do you know you hip is shfitfted to the right? You can not see your hip it is deep joint, please give us more informations so we can helpful. Thanks.