If the pain is at the base of your thumb it could be cartilage issues, as in its wearing out. If it is between the base of thumb and index finger might be small tendon strain. If your hold your hand still and flex your thumb back and forth and there is pain then its probably the first. Might be a little arthritis in that area.
"I would switch to a two handed backhand but
that won't give me a free hand to hold the beer."