If you go and tell your doctor you're having trouble with a statin, they should have you try a new one, yeah. Some might need to get clued in on pitavastatin, as it only recently went generic and insurance companies really didn't want to approve it before this due to the cost and wide field of generic statins, but it tends to have one of the best profiles when it comes to side effects.
The PKCS9 inhibitor monoclonal antibodies are an option for most people if they show intolerance to multiple statins - insurance will usually relent at that point.
If your doctor isn't willing to work with you to find the medication that works best for you, then find a new doctor.