The TMJ Association advises against using the over the counter mouth appliances and they recommend that even prescription splints be used only temporarily. The worry appears to be that the splint could shift your bite to a new even more uncomfortable position. Some TMJ sufferers do get substantial relief from them, however.
It sounds like you should try the full range of other treatments (gentle stretching, meditation and relaxation techniques, prescription meds, etc.) before you go for the splint. Unfortunately the field of TMJ treatment is still in flux and you'll get different opinions depending on where you go.
For more from the TMJ Association: http://www.tmj.org/treatments.asp