Help! Bloody chicken butt (literally :()

Third day of having chickens. Picked up a couple from an established flock, both ~ 2 years old, so not laying crazy-fast, but that's ok. Literally third day of having them around. First two days were fine, but this morning one of them is hiding in the coop, won't come out. When I was checking the coop for eggs, I saw that her butt is seeping blood. She keeps making straining motions, like she's trying to poop, and bits are flowing down, over the blood and everything. She looks terrible... I have no idea if the other one pecked her (wouldn't we hear crazy noises? and they've been fine so far), or if she ate a screw or something (house is pretty new, and the construction crew wasn't great on cleaning after). What do I do?? Do I try to clean it and examine (=stress to her), or just let her do her own thing? Feel terrible for having this bird suffer

Read some online after frantic searching, she might be egg bound. We gave her a hot bath, and put some lubricant on and in her vent. She's in a dark box now. Not drinking, not doing anything, just standing there, flexing her vent (and, I'm sure, bleeding some more). Not sure what else to do at this point...

I hate to be the bearer, but I've not been able to revive one from being egg bound. But some good news is she may not be egg bound, coccidiosis or an extreme case of internal worms could be the culprit. All of the above can cause bleeding like your hen has, you'll need to get some fowl wormer down her asap, also a coccidiosis treatment, it's rare in adult fowl and we treat ours when they're chicks so I'm not sure what treatments are available.

The first think I thought of when you said bloody but was coccidiosis. It doesn't look like she is being picked at, but definitely keep her isolated...their picking of each other makes the bleeding worse.

Thanks for all the replies! Figured I'd post an update. The lady that gave us the chickens was super nice and swapped the sick one for a new one. The next morning, we got 2 eggs for the first time. I'm pretty sure that in all the three days we had the original 2 chickens, only one was laying. We've been getting 2 eggs every day since. I haven't talked to her in a few days, but last I heard, the bird was getting worse. So yeah, I'm pretty sure she was egg-bound, and all the hot baths and bum massaging I tried didn't do much... Can only hope I never encounter this again, because it sucked to feel so helpless when the bird was clearly suffering.