K. ~
I'm an OB nurse and have seen women deliver while being sick. Sometimes, dependin on what it was, they've been induced. What are you sick with? It is sinus/upper respiratory? or more like vomitting? Stay hydrated, get as much as possible. There could be medications that you can take to help you feel better, depending on what you're sick with.
The baby will not get sick from you. If other family members are sick when you deliver, make sure they wash their hands well before they touch her, and maybe even wear masks so they don't breathe on her (the less exposure from others, the better).
Also, when you do go in, if other friends/family members are sick, please ask them not to go to the hospital to see you and the baby...they can see you both when they're feeling better. There's alot going around already, and other patients may be very susceptible.
Good luck! hope you feel better!
D.