I had the same thing, super painful, super heavy periods and also got perscribesd mefanic acid. Like you say it worked amazingly for a while but I also became resistant to it. Going on the pill didnt help me, infact I got a side effect where I got raw patches on my cervix and then bled all the time with pain (lame to the max I had to have a very aukward procedure to quatersize them) however! I then swapped to the patch which apparently has different levels of hormone and because you wear it all the time, releases it differently. This has lessened the heavy periods a bit but to be honest what I do to avoid being incapacitated all day is alternate between paracetamol and mefanic acid (as in for each period), pile on hot water bottles and if I can take some sleeping pills and sleep for as long as possible untill the pain goes away!
However if I were you I would also ask to see another doctor as before all of the above my doctor sent me for an ultrasound to check for polysistic ovaries. They also insisted on doing STD tests but then they always do for any kind of down there stuff because they assume all people our age must have loads of unprotected sex.
Anyway I hope things improve. Try the alternating thing, I hope you find somthing that works.