It's going on eleven here. I will just summarize and wrap up what I think might be going on with this hen and what I believe we need to do to treat it. I believe she needs help immediately or she may not live until morning.
I am not there, wish I could get hands-on so I know first hand what's going on, but here's how I see it from the pics and the bits of info you've supplied.
I think she has a plugged vent and is constipated. Poop is backed up, and it doesn't need to be that way for too long before it can kill a chicken. So first step is to open the plug. If we had more time, I'd advise a teaspoon of coconut oil orally, and another in an hour, but she needs faster resolution. That's why I advised a molasses flush. It will stimulate diarrhea and it should open her up within an hour.
After than, another Epsom salt bath to gently debride the external vent area. This is the necessary first step in treating infection. Care must be taken not to lacerate or perforate the tissue inside her vent as it may be swollen and exposed. I believe some of this could be infected for some reason we probably won't be able to figure out. This will cause the tissue to inflame and swell and possibly bleed, all contributing to blocking the vent. I'm pretty sure infection is already well underway, and if not, it is inevitable.
Therefore, you will need to start her on the doxy. Give her 50mg now. In the morning give her .25mg and the other .25mg in the evening. You will probably continue it for a full ten days.
Each day, twice is better, she should get a salt bath and clean away any necrotic tissue. Treat with Vetericyn wound spray and a topical antibiotic ointment. She may need more oil orally if she is straining to poop.
I hope we got this in time. I'm so sorry if we didn't.