I have TMJ, recently diagnosed, mostly affecting muscles more than articulation. And also I'm having tinnitus that seems related to trigger points in masticatory and neck muscles (I'm not sure if one of the sounds could be that or hearing loss related, though).
I've got to eliminate one of the sounds by means of physical theraphy for back and neck, and trigger point therapy (self applied) for trigger points. The other seems to be at the very minimum influenced by the points, but it's related to zones with lots of muscle knots, and sure I'll need a splint and lots of treatment for that muscle in order to beat it.
I suggest you to google all that you can about trigger points, myofascial pain, and how they relate to tinnitus, especially the TP's of the masseter, sternocleidomastoid, temporalis, lateral pterygoid, and even the trapezius (it absorbs tension when you clench your teeth at night). Several of these points can refer pain signals both to middle ear or inner ear, so they can create tinnitus that is either low or high pitched, or both kinds if you have different points in different muscles.
There's a book called "Trigger point therapy workbook" by Clair Davies who teach you self massage techniques for this points. If you try this, be careful, the degree of pressure he advises is not always the best for everyone. Try to start softer and raise the pressure day by day.
If trigger point therapy does something for your tinnitus (at least changing the sounds) try to get a few sessions with a proffesional so you can get the feeling of the theraphy and doing it later when you need it at home. You could go to a physical therapist or even better, an osteopath.
I hope this has been of help, if you find that your tinnitus is related to these muscles and have more doubts, ask me, I've researched quite a bit about it.