I'm sorry your girl is sick. If it's a reproductive issue, the Calcium will not fix this issue nor will it help her much but it won't hurt to give it to her for a few days to see if she passes an egg to help rule things out.
I would suggest antibiotics if you have them to help with a potential bacterial infection to make her more comfortable. If her belly is hard, she is probably suffering from EYP or another reproductive issue.
We had a production breed that went down quickly, looking similar to yours, and seemingly recovered for a few months with the help of Calcium Citrate with D3 and oral antibiotics. She recovered enough to be a chicken for several months before it happened again. But she never laid an egg in this time. The next time she regressed it was severe and with no hope of recovery we had to end her misery.
If they cannot forage, scratch, are inactive, acting lethargic, laying around, not really showing an interest in food or others in their flock, it's difficult to watch them in this state.
I've learned that bathing a sick chicken is stressful so you will have to assess if that is necessary or if you can clean her bottom without sticking her body in the sink. Soapy water (Dawn) works well.
I wish you luck. I hope she recovers.