It doesn't matter if you're "actually" having high levels of pain or if you're just "hypersensitive", strong pain is something you shouldn't just be putting up with, especially if it's affecting your ability to function in any way.

I've had horrendous crawl-up-in-a-ball-and-hope-to-survive cramps that lasted for days, shortlived sharp shooty cramps, dull rolling cramps that go for days, no pain at all. In the horrendous crawl-up-in-a-ball days, pretty much none of the anti-inflammatories on the market (ponstan, nurofen, naprogesic etc) were really achieving an appropriate level of pain control, and I also would experience vomiting, diarrhoea, and headaches at the same time. In the end what worked for me was a Dong Quai herbal formulation (from memory it had some other women's herbs like black cohosh, squaw vine and some other bark in it as well). I would start taking the DQ around the day I was due and took it three times a day for the first half of my period. Worked a treat. They've since taken this (and other dong quai products) off the market because of issues around strength and quality of the imported dong quai used in the formulation, but if you saw a good naturopath or chinese medical practitioner I'm sure they would be able to help you with a similarly effective formulation.

ETA It's totally worth seeing a good GP who specialises in women's health or even a gynae to rule out any other problems that might be causing the pain, rather than just reaching for stronger and stronger meds.