We had also recently joined 4-H for rabbits and chickens with my eldest daughter and were heartily welcomed into the group. The group had amazing leaders that were fun and friendly to us newcomers and provided lots of advice.
As she kept squeaking I finally called the leader of our rabbit/chicken club and told him the problem. This man's name was Marvin and he was the kind of no nonsense man that you often see in farming. He was a bit gruff but the kids loved him and he was fiercely devoted to teaching the kids. He had been raising rabbits chickens ducks and turkeys for more than 20 years and had a wealth of skills.
After listening to my story he bluntly said that he had seen chickens do that before and it was most likely due to my hen having eaten a mouse. Chickens can't tear things apart so when they get ahold of a mouse or snake they swallow it whole! Well I almost couldn't believe it! I just had a hard time envisioning the chicken eating a whole mouse. I mean how could she get her beak open wide enough?
He told me not to worry, within a few days the mouse would be digested and the squeaking would go away. He, of course,
turned out to be right and the hen went on to live a long life, but it proves that the best reference you can possibly have is an experienced person. Because I can tell you no chicken raising book I ever read had information on squeaking chickens!