Previously broken thumb support for basketball help?!

I had a thumb fracture and a small piece of my bone at the joint between proximal phalanges and metacarpals broke off. This piece got back in place with a small screw, but the surgery was late and the piece is not in the perfect place.

Anyway, the idea is that my thumb is much more sensitive even to light blows and I've developed fear of injuring it again. Is there any kind of support for such cases? Such that immobilizes the joint either completely or offers really good support (so that upon contact with the finger tip the joint wouldn't be twisted). It's my left hand and I don't do a lot of ball gripping with it (partly due to discomfort of that joint).

Any ideas would be welcome.

Oh and I tried some sticking-plaster tapes - it did help until yesterday's practice. A small hit from the ball and I'm thinking of completely quitting basketball again (it's a hobby though, my pro sport is different) :(