I'd give her the Amoxicillin.
You can give her the Calcium directly, just pop the pill into her beak and let her swallow it.
Make sure she's drinking very well.
Do you have a thread about your hen? If you do, I can't find it.
Can you gently feel inside her vent for any egg shell pieces?
Is she pooping?
I'd give her the Calcium to help with contractions, but if she had egg material or an egg break inside of her, then I'd also start her on an...
@HeathenHavenHomestead I'm sorry about the loss of your hen.
I agree with @azygous unless you get a necropsy through your state lab or do an informal one yourself, the reason will remain unknown. But there is a reason. I also agree, very likely a reproductive issue.
Looks like there may be some blood on the membrane back in post#2 which was Friday.
This is first time you've noticed a blood clot ?
I'd work on giving the Calcium daily for a few days to see if she's able to expel more shell material, a membrane or an egg.