I am sorry to hear about your hen. The first one I lost was last year. She wasn't close to being a favorite (she was obnoxious and mean--even at a day old chick), but I was her mama and I sobbed for days. Even though the vet volunteered to euthanize her, we brought her home to let her be with her flock for a few more hours and then my husband did the deed with a hatchet. We figured, better get comfortable with killing them because eventually it will be an emergency and no vet available. (The gassing of them is inhumane -- please read the threads here. I would never suffocate one of my babies that way--they deserve a quick death at our hands if need be).
Since then I've had a frantic eggbound hen die in my arms (heart attack) and we just had to take my favorite hen out with the hatchet last weekend. It sucks, but I get that it is part of what I took on when I got chicks. I am grateful that I was able to cuddle them close and talk lovingly to them when they died.
It gets easier with each hen, but it still hurts. It helps to know you did as much as you could to help them, and to help them pass when it is time.