Why do I feel my pecs hurting when doing back exercises?

The back exercises you mention all involve arm action – which automatically engages the pecs/chest area.

For women the soreness is sometimes increased if we have larger boobs (my experience), but the benefit is more lift as you gain muscle tone.

Just pace yourself and increase your effort gradually.

The band pull downs will specifically exercise your pectorals, so that’s probably the main reason that they’re sore.

I suggest taking a day off if your pecs are sore, to allow your anabolic processes to rebuild and increase your pectoral strength.

Try doing some lower back stretching, and then do some lower back curls.
After the curls, do some downward-facing dogs, to relax that muscle group.

Hopefully you’re bending your knees when you do your deadlifts.

Any exercise where you are pulling down with your arms from over your head (pull ups for instance) are impacting the pectoral muscles.