As someone who decided to ignore the doctor's advice and take NSAIDS and ended up with ulcers: please, please, please: follow your doctor's advice. Even if you think it's worth it to take it just a couple times to alleviate the pain: IT'S NOT.
I totally understand not taking Tylenol: it doesn't do a thing for me either. The problem is avoiding opiates, obviously. There are other pain relievers that you can take and it's best to have a serious discussion with your doctor if you have chronic pain that needs to be managed.
My doctor prescribes Tramadol (Ultram) for me for migraines/cramps/severe pain. It's the only thing that works for me. I know this tends to be a solution for a lot of weight loss surgery patients because it's easier on the pouch, but you have to be very careful because it's a low-level narcotic. I take it only when needed and it has been a good solution for me.