Thanks for your query.
Stiff and painful thumb and pointer finger cold
be due to arthritic changes or tendonitis
.I would suggest getting this evaluated by an orthopedician for an accurate diagnosis and appropriate management. You may get the X-ray/MRI
of the area affected under his/her guidance.
Meanwhile you can take anti-inflammatory drug like motrin
to reduce pain and inflammation.
I do hope that you have found something helpful and I will be glad to answer any further query.