The sound is called as tinnitus. This is likely to be adverse effect associated with Cymbalta. You may wait for another week, which may resolve it spontaneously. Otherwise you would need to consult an ENT specialist for the following investigations;
1) Audiometric evaluation
2) A complete blood cell count, an autoimmune panel (ANA, sedimentation rate, rheumatoid factor), and thyroid function tests.
3) MRI of the brain and internal auditory canals.
Following are the other common causes of tinnitus;
1) Exposure to persistent loud noise.
2) Ménière's disease.
3) Ear wax
4) Eustachian tube dysfunction
5) Environmental allergy
6) Blood pressure fluctuations
7) Diabetes and thyroid conditions
8) Medications are an extremely common cause of tinnitus
If you are taking any anti-inflammatory analgesics for any kind of pain like toothache, they should be stopped. All aspirin-containing products and nonsteroidal anti-inflammatory drugs should be discontinued. Supplements like vitamin A, vitamin C, cyanocobalamin, and nicotinic acid, with magnesium, zinc, or copper are suppose to help.
Read the resource on tinnitus;
Please feel free for your follow up questions.
I would be happy to assist you further, if you need any more information.