Exercise for bad hips

I've been born with hip dysplasia and when x-rayed at 14 told it didn't get completely right (sadly I have no other info). I was told not to jump and run long distances, but that strenghtening the muscles there will help. The problem is, I seem to have more and more problems over time, especially in the past 3 years. Sure, part is becoming a lot more active upon discovering a new hobby and new friends while not having experience what can I afford to do and what not, but I have a feeling they are getting increasingly sensitive. I decided I finally should act on the old advise and strenghten the muscles, but anything I try ends up hurting my hips sooner or later. I want to know what sort of exercise would be best and if the pain is indeed something I should be careful about or merely something that I should expect and not be concerned about.

The pain is caused by a variety of things from bad shoes or running with a backpack to repetitive exercise that puts strain on the hip while requiring to stabilise or twist. Interesting thing is that it can be something I've never had problems with, but one day it clicks and.... It can take anywhere from a day to several months to get better, with an increased sensitivity period afterwards. There's no relief position, simple movement makes it worse only a little bit, but putting weight on it is not a good idea. As far as I'm aware it happens to both sides

I'm not sure what to do. What would you reccomend?