If I'm treating someone with sepsis, is it likely i'll catch it?

Doubtful. Sepss is due to bacteria in the bloodstream. Even with direct contact, transmission is rare. In general viruses are much more contagious than bacteria, so wash your hands, but don't worry too much.
No. It's unlikely to be contagious unless the sepsis is caused by an airborne type of infection. Wash your hands frequently when caring for someone who's ill and avoid touching your face.