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Hi there ...
As you mentioned you are on birth control pill , and cramping along with that moves underside the hip bone , that increases with stretching , coughing , this need evaluation to rule out the possibility of DVT ( Deep venous sthrombosis) as contraceptive pills increases the chances of DVT .
I will suggest you to have Doppler Ultrasonography of leg / thigh to rule out DVT .
Once ruled out , then no need to worry , simple Hydration , and pain killers will improve it .
Good luck .
Positive feedback will be appreciated .