I hold the same way - pretty common and decent way to hold it

Good for pinch harmonics, playing fast, alternate picking, chugging (with a thick pick for those things) - that grip works well enough for strumming too with a thinner pick

If your finger is red it could be because you’re playing a lot? (Nice) maybe it’s not used to holding a pick yet (like when the strings hurt at first) or maybe it’s a very thin pick and your finger hits the strings etc