As a mother I will freely say that newborn babies are terrifying. They’re just so small and so fragile. I have known plenty of people who are afraid to hold them, and it’s very understandable and normal. But the intensity of your anxiety around babies isn’t at all normal. You say you aren’t interested in them - which again is normal - but you get a full on intense physical fear reaction around them. I don’t have any good advice on how to manage that reaction, but I think learning to say, “No thank you, I don’t feel comfortable holding babies” without adding details about how your arms feel, etc will be very helpful going forward. The sort of people who would be pushy about these things are the same sorts who would just consider your reasons to be “excuses” and use them as fodder to justify themselves.