If having sex hurts stop having sex. You could be making more a problem for yourself in the future by causing unnecessary pain and injury now. There are plenty of other ways to be intimate without hurting yourself.
I would also say try and stick with mirena - there are settling in grumbles but every single thing you try for managing periods has settling in time with side effects to some degree.
As your periods are so painful - just imagine the utter relief when you no longer have periods. It is indescribably fab not to have periods and period pains, but it does take a few months for the mirena to work its magic.
It is such a faff having it put in - and waiting for it to settle, but my god it's so worth the wait.
And at 16 with a whole life ahead of you of painful periods if you don't give it a chance, it it even more important that you try and cope as best you can with the next handful of periods. It is hell having them - but if you get mirena removed you will still have them, so what's the point in not giving a mirena a chance to work.
When you do get older the GnRH drugs are possibility - and trust me, the mirena is nothing compared to the side effects of GnRH on the body !!!
If you stick with it, by summer holidays you could be period free.. with no fluctuations in the monthly hormone cycle, no PMT, no period pains and you get your life back.
I had bad periods for 30 years with endo- and couldn't believe how great the mirena turned out to be in the end. You owe it to yourself to stick with it and give it a chance. Be strong - it is worth it.