I'm not sure if I can connect the chest pain with the tremor or another neurological cause
A fine tremor occurring at your age, with no other neurological abnormalities is usually benign essential tremor. This is especially likely if someone else in the family has it. Depakote will make it worse, as it is also a cause of fine tremor.
Tests for thyroid function are important as well as a few tests to ruleout some rare but treatable disorders like Wilsons disease. Treamtent is with medications such as beta blockers or primidone. The hyperhidrosis is less clear, but it would be interesting to see if it diminished when, for example, a beta blocker was succesful in treating the tremor. If not, more specialized testing may need to be done in an autonomic center such as the Cleveland Clinic Autonomic laboratory.
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