Hello,
I am sorry about your chick.
We went through this last night. We have only had chicks for a week, but one was sick and clearly suffering. My husband is such a gentle soul, but he had to end the poor thing's suffering. I know he is really beating himself up over it, and feels tremendous guilt. He did the right thing, and you did too. I don't think that I could do it - I get too emotional and attached. Doing the right thing isn't always easy.
I am sorry about your chick.