Welcome to the world of guitar playing.

I once read a tip about applying metholated or surgical spirits (they're the names of them in the UK, but might be different in the US or elsewhere) to the fingertips of your fretting hand. Do this several times a day but don't play the guitar without washing it off first. I have no idea how well this helps, or if it works at all.

Don't play guitar immediately after doing something like washing pots, as the skin is softened by this.

Don't play to the point where a mild discomfort, which goes away within a very short time of pausing, becomes what could be described as pain.

Other than that, it's just a case of waiting until the callouses form on the fingertips.

I would recommend light warm-up exercises when you first play, though, especially if you have arthritus in your hands. Gentle Spider exercises fairly high up the neck, or slowly playing pentatonic scale shapes would be good for warming up.

I would also advise you to be very careful when doing any finger stretching exercises: make sure you've warmed up and avoid pushing yourself to get that "extra bit" of stretch.

Playing dexterity takes a long time - injuries take less than a second.