My mother is on blood thinners but is in constant pain from arthritis. Is there any pain medications she can take?

This is most definitely a question for your Mother's doctor. There are medications that are safe to take with blood thinners, and some that are not. Those that are not OK, dependent on dose of both blood thinners and medications are Aspirin based and NSAIDS (non-steroidal anti-inflammatory medications)such as Advil, Motrin, et al. Do not accept the opinions of lay people. Blood thinners are major; as an RN I saw more complications occur with blood thinners than with any other medications. Do the lab work that is advised; know and report the side effects, and run all other medications past your Mom's MD.