I work with newborns and often with premies. Of course, I also work with their mothers and often their older, but still very young siblings.
At our agency, we are required
to let them know if we are sick. And we are required to then NOT work with patients. A cold or tummy bug could be devastating to a newborn or preterm baby. Not to mention make things very difficult for a new mother.
I honestly think it's very rude to show up to work sneezing and coughing, barfing, having diarrhea or otherwise contagious. There is no "strength" in toughing it out, when it will result in making either your co-workers or your clients sick. Nobody is that indispensable. A day or so away from your job isn't going to cause the world to stop turning.
So, no, I don't feel guilty when I have to take a sick day. I'd feel more guilty if I went to work and could have made other people ill.