I'm prescribed mobic (meloxicam) 15mg 1x a day, and it's not working. I haven't taken a dose since 6pm yesterday. Is it safe to try OTC naproxen today instead?

Yes. NSAIDS differ in responses in different people. It is rational to try different ones before giving up on them. Also some require more than just a day or two to see if they,'re effective. Newer ones like Celebrex (celecoxib) are easier on the gastrointestinal track in some but not all people.