Cat’s bottom looks swollen, has poop on it, won’t let me touch/look/wipe.

From the photo the cat’s testicles have lost hair and are inflamed, likely from estrus raising male hormones and frequent rubbing and stimulation causing redness and swelling. Also check for a wound – a fight injury the cat licks can become a pus infection; clean with iodine and fit a protective collar to prevent licking.

If it will not let you touch it, take it to the hospital to clean and treat the wound. After recovery, schedule neutering surgery as soon as possible.