Am I in the wrong ?

So as much as I want my sister to be there when I have my baby, she’s sick. I don’t want anyone sick around my newborn and I’ve constantly made that clear to everyone that if you’re sick I don’t want you to see my newborn until you’re better. Well my mom is making me feel crazy basically telling me that it won’t be the end of the world if my newborn gets sick because he’ll have all the nutrients from my milk so getting sick won’t be a problem. My sisters a kid(7 going on 8), she doesn’t cover her mouth when she coughs, she puts everything in her mouth, doesn’t like washing her hands at all and when she does it’s usually half assed (rinses water), and refuses to take any medicine.

So all of that in mind, I don’t want her to get my newborn sick. But my mom seems to think I should just suck it up and let my sister see him anyway because it’ll hurt her feelings if she doesn’t get to. Am I wrong for not wanting my newborn around anyone that’s sick ? Like honestly am I being over dramatic about this ? My baby will be here in less than a week and I’ve been stressing over this.