TMJ can be a cause of tinnitus, and some TMJ specialists say bite splint therapy can help. But I think it should be a last resort as it is very expensive (at least where I live), isn't guaranteed to make the tinnitus go away, and can change your bite so much that you may need braces. There are night guards (stationary splints) you could try. Like Cullenbohannon said, you should consult a dentist. Here's what the TMJ Association recommends:
1) FIRST, try eating soft foods, using ice packs, and avoiding extreme jaw movements, like yawning and gum chewing. Short-term use of over-the-counter or prescription pain medicines may also provide relief.
2) AVOID treatments that cause permanent changes in the bite or jaw. This includes crown work, bridge work or orthodontics to change the bite, grinding down teeth (bite adjustment), or repositioning splints.
3) AVOID surgical treatment, where possible. There have been no long-term studies to test the safety and effectiveness of these procedures.