If your talking about a chick it could be pasty butt, clean the poop away as soon a you can (wet or dry paper towel) then put gel vaseline on and keep doing this if it keeps happening, but if your talking about a adult well sometimes they will get dirty and you cant do much about it,if it an outdoor the rain might help but i wouldnt give them a bath because it might mess up their feathers, if all else fail's just try to whip the chicken's feces off of the chicken and keep her/her healthy and happy.
Welcome to BYC. You can learn a lot of info that can help you take care of your chickens here. It is also a place to share your knowledge with others. You might be dealing with a fungal infection called vent gleet, which can cause runny smelly poops, red irritated skin, and it can cause white or yellowish patches. Here is some info about vent gleet: https://www.tillysnest.com/2012/12/vent-gleet-prevention-and-treatment-html/
Thank you for responding. I'm super overwhelmed by this. Her bottom is red and swollen like a water balloon. She has labored breathing, feathers all puffed up, eyes semi open. I bathed her bottom yesterday and clipped the feathers below her vent. The vent looks completely normal. I feel so helpless I could just cry. Any help you can give me would be greatly appreciated.
Is it possible she has been bitten by something? Spider, centipede, snake?
Try to keep her hydrated at least, even if you have to use an eyedropper. Chickens are really hard to diagnose. You may have to separate her if the others start picking on her.
Has she laid an egg recently? I have not heard of egg binding causing that appearance, but anything is possible. I would check for a stuck egg.
How old is she?