The same thing happened to us when my baby was about 6 weeks old. My older DD ended up hospitalized because she was so dehydrated from the fever. Not only did my newborn not catch Croup but she didn't catch anything else from being in a disgusting ER waiting room. My older DD weaned about a month before the new baby was born so that wasn't an issue but I bet your little one will be fine.
In my experience, my kids when newborns didn't get sick at all regardless of other family members being sick in the house. I particularly remember having a horrible stomach virus when my oldest was a couple weeks old and I was terrified she was going to catch it. We just laid in bed for a couple days and I nursed her every time she woke up so we just slept for a couple days next to each other and she never caught it.
Good luck, I hope your LO is feeling better soon!