Let go and regrip. Get fast at it, develope that skill, look into good YouTube instructors that emphasize grip fighting (Stephan Kesting has this with Emily Kwok, Chewy at chewjitsu has some good stuff too iirc, and probably lots of others). You can also work on the toughness of your fingers and grips but there is no hurry for that. Some of that will be trained but some may just be generic and you will have to adapt your game if you want to sustain your training.
It doesn't hurt to learn about how to tape your fingers (I believe it's covered in the FAQ for this sub) but I don't think that's the problem you are having. Taping is usually used more to support the joints than to protect the skin of your fingers.
