Yes, I agree with Ellen (by the way, welcome to the forum!), the lady is either a hypochondriac or is under a misconception. This is common in older people. My mother was always and forever predicting doom because I was always touching and kissing animals - especially the parrots! To this day I am surprised they did not learn to say "You are going to catch psittacosis!" because Lord knows they heard it on a daily basis!
Tell her that the only disease a human would catch would be psittacosis (don't use the newer term, chlamydiosis because, most likely, she doesn't know it by this name) and that your bird has been tested for it and it doesn't have it. Neither is strictly true but, sometimes, one needs to stretch the truth a bit to make the information more accessible.