Caring for sick kid?

My ND texted me today 10 mintues before they said they would come pick me up to take me to a nanny share with another family, saying their NK is sick and asking me to take the kid to the doctor with the mother. They said he has a spiked fever and “jerky movements”. They asked me to basically get to their house in 10 mins ( they know I don’t have a car) and go to the doc with the mother and baby. I’ve been really sick on and off the past few months, and I’m concerned with getting sick again especially if the child has a fever. I don’t want to be mean or put them in a hard spot, but I just feel uncomfortable going to the doctor with a sick kid and being in a doctors office with a bunch of other sick babies. It’s also frustrating they asked me to somehow get to their house in 10 mintues meaning I’d have to uber over there, rush to get ready and then get in the car with them and go to the doctor. ND works a lot but it’s like, if your baby is sick, suck it up and go to the doctor with your wife? Why do I have to be the one to do it? And I feel like it’s a lot to ask of me to be subjected to the kid if he’s really sick, I’ve gotten sick from him in the past which is okay I mean it happens it’s not a big deal, but knowing he has a fever and then asking me to join just feels like a lot. Am I overreacting? I feel bad not helping them out but it’s a personal boundary I feel like I need to set, which I have trouble doing.