I honestly don’t even know how Percy got it.
Percy probably got sepsis from another infection first. Usually, sepsis is a secondary infection, just like with people - she might have had a wound or an internal issue that caused her to develop sepsis. If she was egg bound, you might need to watch out for something called salpingitis, which is an infection in her oviduct.
Has she laid something looked like an egg but was rubbery or maybe pus-like and solid?