What is the best over-the-counter medication for trigger thumb?

Anti-inflammatory. Trigger finger or thumb is an irritation of the tendon. Usually rest and an anti-inflammatory like advil or Aleve (naproxen) will help. If symptoms persist consult your doctor.
NSAIDs. If you can tolerate non-steroidal anti-inflammatory medications (nsaids), symptoms can be improved with occasional use. Ibuprofen or Naproxen are commonly available over-the-counter medications that can be very helpful when symptoms flare.

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Please help! What is the best OTC medication for trigger thumb?

Any pain med like -- Aleve (naproxen) or ibuprofen, etc, whichever works for you. It'll give you some pain relief but do nothing to get rid off the problem altogether. Generally surgery is needed for a more permanent relief. Read more...
None work. Pain meds and nsaids will not help. A local cortisone injection may work. If not, surgical release is needed. Read more...