You are going to be interrupted endlessly at the hospital. Chances are you will also have an IV in your hand at least part of the time, which can catch up in things. My recommendation is to put your supplies into a divided Rubbermaid-like container and the whole thing (including your hoop) into a tote bag. I only use little plastic bags for blended threads - otherwise, it's the floss cardboards. Mark the number clearly on two sides so if it wears off on one, you still know what you have.
Good luck! I've never been able to work projects while a patient in a hospital, which sadly, has been frequent in the last year, partly due to that IV. I just read, listen to audiobooks or music.