Of course, not a problem

so it’s funny timing, our dog went running (intensely chasing an RC car!) on the asphalt and he tore up his fingernails pretty badly. Down to the quick and cracked quite a few of them and it’s had him out of commission for about 3 days now. Poor guy just limps everywhere and our other dog accidentally stepped on his paw and sent him into a yelp and further limping. So anyways my point being, broken toenails and exposed quicks must be pretty painful for an animal who really utilizes their feet all day, even to rest. So I’m not surprised it hurts her to walk on still, especially when she keeps bumping it.
Hang in there, hopefully she will start to use it more and more each day as the nail grows back. The red part is her quick and when you compare it to the other foot, you can see how exposed it is and how much nail she lost. I would bet that really is painful. I don’t think it’s abnormal really for it to be red, especially if she keeps bumping it and irritating the tissue. It doesn’t look bad to me, but keep checking it a few times a day. I would not start her on any antibiotics, but keep up with a triple antibiotic ointment if you can. Signs of infection will include swelling and possibly pus. Chicken pus is hard and the texture of a cheese curd. So if you notice any hard swelling around her toe, that would be infection. Also, did you get to check the underside of her foot by chance? Make sure there isn’t a cut or something there making putting pressure on her foot painful.
Your hen with the hiccups, do you have a video? Is her crop emptying overnight? And has she had a break from laying yet to molt? You might consider starting a new thread for that hen under the emergencies/injuries section, just to get more relevant help if needed since this thread is about broken toenails.