I can't see the pic very well, but this sounds like a prolapsed vent. I have a hen inside right now for a prolapse. I really have no idea what I'm doing, but she gobbles down scrambled egg and yogurt with extra calcium in it. Could this be what has your hen in distress? My hen also lays eggs with blood spots on them. I didn't know that's what it was until I watched her lay the egg and picked it up while it was still wet. I could rub them off, but when it dried the spots were permanent. Could this blood be from intestinal parasites? I think I'll treat my hen anyways. She has the protrusion that I've tried putting Prep H ointment on, but the ointment wont stick due to the moisture already present on her behind. I am able to push it back inside, but she still has the urates dripping out and poops out fully formed stools.
I hope your hen does better soon. That must be painful for her.