Is there anything I should know? Like, am I going to die?

I've been scratched by my cat before, but not this deep. My girlfriend accidentally startled the cat while he was squirming in my arms, and he clawed one of my fingers HARD as he bolted away. I ran it under very cold water immediately, and I put a band-aid + neosporin on it soon after. I'm not going to catch anything from the cat am I? He's had all of his shots.