Newsflash - babies were made to breastfeed, breasts were made for nursing!
My response to this mom was this:
Aw man, that's rough, but your DD is a newborn still!!!! Breastfeeding is recommended for at LEAST one year by the AAP, and TWO by the World Health Organization.
Tell them that your doctor said that formula is the WORST thing to give a sick baby - don't they give pedialyte for puking/diarrheal babies? Well... it might make headlines, but pedialyte was made as much like breastmilk as it could be, because breastmilk is BEST.
Just keep your head on straight, tell them it's not up for discussion, stop taking their calls, walk out of the room if they start in on trying formula, nurse your baby in front of them, GET YOUR PARTNER'S 150% support - if you need him to deflect some of the pressure, GET IT. He can take the heat for a while and hand out kellymom.com pamphlets on breastfeeding benefits. Print off pages from kellymom, the AAP, whatever. Tell them when they're ready to shut up about formula, they can see the baby again. Until then, sorry!
Stop saying anything at all about it - but don't let THEM talk about it. You don't need to make excuses for nursing your child!!
I know lots of other folks have gotten pressure about breastfeeding, the #1 thing is - you know what is right for your child. They got to parent you, now it's YOUR TURN. End of discussion. Oh, wait, there WAS no discussion!! You're right!!
Sorry, I get a little heated about this topic and I'm sorry you're having a rough time and a sick baby!! Hang in there!!