I have read that 'magnesium' deficiency can cause ring in the ears - also there seems to be a connection with lyme and low magnesium. - just a thought.
Gorbs
I haven't had the ringing in the ears that you are experiencing, but it's a symptoms some people get. Someone else here may be able to answer, but don't worry -- keep treating and pursuing the illness until you are well.
You have, in my non-medically-trained opinion, done the exact right thing by getting tested and treated. You don't say if you are being treated by your PCP or a Lyme specialist -- Lyme specialists are likely to treat longer, and the more advanced view of Lyme is that longer treatment is justified. Non-Lyme specialists rely on a few weeks of antibiotics and you're done no matter what your continued symptoms.
Let us know if we can help further, and continue to be aggressive about getting diagnosed and treated. (Were you tested for coinfections that sometimes come with Lyme?)