Was I wrong to freak out?

My fiancé and I very recently had our first baby. Still trying to adjust to parenthood, I just noticed we were beginning to run low on a few things so we decided to out for a quick trip to the store. Everything was going smoother than expected for our first "family outing". There were no crowded aisles and our 3 week old son was sleeping snuggly and peacefully in his seat. Then while we were waiting in a check-out line, we ran into a friend we hadn't seen in a few months and got to talking about our son and her 2 and a half year old, who she had in tow, and she mentioned that her little girl had just semi-recovered from the flu, only a runny nose left. As the conversation was coming to an end, the girl asked to see our newborn, which I was completely fine with, so her mother lifted her up for a peek. Then my friend told her little girl to touch my son's head and feel how soft his hair was. I watched in horror as this girl's hand, which was snot covered from wiping her nose with it just moments before, shot out towards the baby. I immediately jumped in before any contact had been made and quickly expressed that I did not want either one of them to touch him, as he is very new and they both could still have flu germs. My friend was apparently deeply offended by this and said I was just being paranoid and overprotective. Here's where I snapped. She then grabbed her daughter's hand, reached around me and tried to make her touch him. My fiancé thwarted her by picking up the baby carrier and moving away. I told her forcefully that we were not going to allow her to touch him and she needed to stop and that she should know better than that to allow a sick child to touch a 3 week old infant. I was then called a stuck up bitch and she told me to never contact her again. This girl had been my friend for 10 years. Did I do the right thing? Should I have been nicer about it, or handled the situation better or am I just being a typical overprotective first time parent?