Hurt my jaw, used a heat pack, now have ringing in my ears. Is it possible that the heat pack has hurt my hearing or is it due to my injury to the jaw?

The jaw Injury! Although the mechanisms are still unclear, 5-10% of all cases of tinnitus, (ringing in the ear), are felt due to head injury (jaw included. It may be a result of damage to the cochlear hair cells in the ear, but unknown. I suggest you speak with your physician. You may need further testing, or a referral to an ear, nose and throat specialist if they don't prefer to manage this type of condition.