Quoted from jackd104:
see a doctor - hand injury specialist.
I would agree, the doctor will let you know exactly what movements are irritating it and provide exercises and therapy plans and/or a brace. Most therapies you can do at home. I had a similar issue to you(index finger and thumb). The key for me was to stop aggravating the injury. Apparently, that makes it worse, can cause permanent damage and increases healing times. It's difficult to do, I wore a brace, did therapy as I did not want surgery. After a couple of months, it went away, I strengthened it and the problem hasn't come back.
I took months, I've read 2-6 weeks healing time which assumes you stop re-injuring it.