This is a tough one. I watched endless TV as a kid when I was sick. Our daughter (also 3) is allowed to watch limited TV dependent on her behavior that day. I've definitely sat with her and watched a few movies in a row...and watched her behavior change for the worse. Too much TV leads to a kid who won't listen, can't sit still or focus, and demands more TV as soon as it's off - true story in our house, might be different for others. We gave in on sick days and noticed that being sick quickly became the go-to reason for watching more TV. Whenever our daughter felt like watching cartoons she would complain of feeling sick and use her best "sick voice" to tell us she needed to watch movies on the couch. So now we stick with limited screen time, lots of books, puzzles, snuggles, and quiet play. Every kid is different. Trust your intuition. If you see changes in behavior after screen time, reassess your limits. It's all trial and error unfortunately. You'll find the right situation for your family.
Reply to Screen Time when sick!?