I'm no doctor, I just play one on TV, and I know this sounds like a default answer.. I would not recommend using aspirin without consulting a doctor first, the reason being aspirin is a blood thinner by nature and it has been shown to have a "common side effect," with ringing in the ears is one of the most common problems.

Are you seeing a General or specialist? One might recommend jaw exercises and a vitamin regime first off.

Mine? I learned to just live with it, the less I pay attention to it, the better.