First up, yes, as above, make sure itās Osteoarthritis!
Second: You can try other NSAIDs. Meloxicam doesnāt work well for my pain (Mine is RA), naproxen (in a much high dose sadly) works better, weāre going over other options for longer-term though.
Have you tried compression gloves? By no means are they miracles, but they help with swelling and provide some support and stiffness to help with pain. When my hands hurt I still cannot use them, but the gloves reduce the pain (and any help is good help with pain!).
Flexeril is a muscle relaxer, wont help much with joint pain. Will help with muscle and tendon pain caused by joint damage, but for the joint pain itself itās pretty useless.
Otherwise, Iām not sure (Still trying to find things to help with my RA!) besides talking with a doctor. Definitely make sure itās Osteoarthritis and not RA or another type of inflammatory arthritis though!!