Every child is so different.. honestly what works for some may not work for others. I have three kids - both of my boys are really good at focusing and playing on their own. My oldest had a Thomas the train set and he would play with that for HOURS when he was 18 months. Before then he had other toys, both boys have never had that "15 minute" child attention span. My daughter, on the other hand likes to be entertained more - which makes her much more challenging in that kind of situation.
When I had a kidney infection and didn't know.. I was delirious with a 105 degree fever and barely functional. I don't usually let my kids watch TV, we go weeks without any, so in that case - I would allow one movie, or a few shows to cover an hour and a half. I stayed nearby and would lay on the couch letting my kid(s) play. Sometimes thats all you can do, it's not the ideal situation.. and my kids did want to play some, I just explained Mommy was very, very sick. I also took a shower and brought my 14 month old in the shower with me. Easy entertainment and it made me feel better. I sat on the floor of the shower and just let the water pelt me.
After I ended up in the emergency room on IVs for 6 hours - the following day my husband stayed home so I could rest. I definitely agree sometimes Dad needs to step up and give you time to recover.
Hopefully you won't be sick often :)