Everything felt good as I played for a few minutes but after I stopped playing a tiny bit of skin came off the tip of my index finger and it didn’t bleed but there’s a red dot. Also, my fingertips are kind of reddish.

This is normal when you start playing bass, even if you've played guitar before. The strings are just that much more massive. I picked up playing bass again during the first lockdown and the first week or two, i just went through the whole process of getting callouses again. Don't overdo things, stop if anything hurts, and apart from that just keep practicing until you've adapted to the instrument. Also, it can help to just play softer and turn up the volume a bit more to compensate.

I guess getting a proper setup will also make a huge difference. Almost all new basses have the strings set way too high to avoid fret buzz. Getting it to a guitar tech will make a big difference in how easy it is to play, and will improve sound and intonation as well.