Thanks for your replies.
I actually am not 100% sure of the exact despcrition, but I do know that all my colleagues fit the same description (with differences in being full time, part time and adjunct). It is quite possible that we are all "instructors" rather than professors. I will definitely look into that.
And yes, the culture does suggest that we are called "Mrs and Ms", not Professor, as I mentioned in the OP. I am not the new hire, my friend is, and this is what I told her.
I am wondering how it became assumed that I was this "pretty young thing", or that I was friends with my students, or wanted them to call me by my first name. That is far from the truth. I have more than enough friends outside of academia, and (quite contrary to what you've suggested) I am not looking to be treated in a diminutive way, nor did I suggest that I wanted to be addressed in such a way. My point is that I feel the term "Professor" sounds much more professional than being called "Mrs". I worked very hard to earn the respect I already receive from my students. BTW, young is a relative term, and in nursing academia, I am considered to be young, but I am certainly old enough to have been a nurse for 15 years, and have been teaching for 4 years. So please don't make assumptions about me