You might want to have that looked at. If it’s sore, try changing your throw. My middle finger was sore all the time late last year. Now I throw kind of like I’m holding a counterweight. I allows the string to go over my my index finger, too, adding support. My finger doesn’t hurt any more. It took a while to get used to but now it’s natural.
New-Skin liquid band aid. I originally started using it on my fingertips for rock climbing. The stuff is awesome. Works like a charm on little cuts, and I put a bit on if I start to get a hot spot. It’s like glue, but less toxic, and you can remove it without another solvent.
Glue and New-Skin is a temporary solution. Build up the callouses the natural way. If it hurts, give it a rest for a bit.
I used to get cuts all the time, but i think a lot of it has to do with your skin being dry. Now i always use some moisturizer before i go to bed and after i shower, problem solved.