Am I being unreasonable?

My husband and I both work full time. We have a 10yr old son and a 2yr old daughter. Every time one of them is sick I have to be the one who takes off work to stay home with the sick child. My daughter has been in hospital 4 times in the last 6 months, mostly for asthma. I'm the one that stays at the hospital and stays home when she is discharged but can't go back to school yet. In April I had all 4 of my wisdom teeth removed. On the same day my daughter got sick with a very high temp and was not able to go to school. The whole week that I was off with a swollen painful face, I had to also take care of my daughter alone. I ended up developing dry socket and was in tremendous pain. My husband did not take time off to help. Now this week, on Wednesday, I had an accident where I fell while carrying my daughter. She hit her head and cracked her skull and was admitted overnight for observation. We came home yesterday and she is back to her busy self and I have to make sure she doesn't fall and bump her head again. At the same time my body is aching from the fall. I skinned my elbows and badly bruised my ribs, arms and knees. It's literally so painful to sneeze or turn over at night. And I can't use my arm without causing pain. But again I'm home alone watching my daughter. My husband just says he will take off next time (but he never does) and I got totally mad and told him that I can't always be the one who takes time off work when things go wrong. That I am also in pain and that I need his help. He is the father of these kids and needs to be present when shit happens. Am I being unreasonable to expect this? My work also gets upset every time I'm off because they have to rearrange everyone's shifts. His boss is a dick, and he currently earns less than me actually, yet I'm always the one who must take time off. I mean, don't get me wrong. My kids come first but heck, surely it can't be me every time. Particularly when I myself am sick or injured. Just feeling so hurt and frustrated at the moment.