What OTC pain medicine is best for back pain.?

Not a best. Nonsteroidal anti-inflammatory drugs (NSAIDS) can help with both pain relief and in reducing inflammation. Examples are ibuprofen (like Advil, Nuprin or Motrin), Naproxen sodium (like Aleve, (naproxen) Naprosyn, Anaprox) or Asprin (such as Bayer, Ecotrin, Ascriptin). Avoid NSAID's if pregnant or allergic to them. In that situation can consider acetaminophen.
No right answer. Everyone responds different to meds, so you may have to try some different ones and see what works best for you. Tylenol, (acetaminophen) ibuprofen, Naproxen are good places to start.