You may have strained your ulnar collateral ligament which should be tested by a physio for the joints stability. Thumb and the small finger joints can remain very sensitive for a few months after twisting injury without any significant structural damage ie tears of ligaments, dislocations. Even so you should avoid any activities that strain and try to massage the area a lot aiming to improve the blood flow and sliding of the ligaments over the bone. If you are having a lot of trouble try a 'buddy' taping where you wrap a tape around the palm of the hand and crossover in a figure 8 style in the thumb web and then around the outside of the thumb. This will restrict the opening of the thumb web. If this seems to work you should keep thumb taped up for a few weeks so the ligament can get a really good rest.

Fortunately these strains do get slowly better.