What do you see?

What do you think of when you see me? Do you think of me as a female? As a Mexican? I know I'm asking the wrong people, seeing how the only people who read this know me pretty well. I'm asking these questions because two situations happened on Friday that kind of pissed me off.
So, I work at an elementary school in an affluent community. 99% of the kids there are white, have stay at home moms AND nannys so that there mom's have time to do important things like go to the gym and get their hair done. Most of the kids' nannys happen to be of Latin American origin. Anyway, so I was at school on Friday and one of the kids was sick so he went to the nurse. After twenty minutes or so the teacher asked if I could go check on him and bring him back if he was feeling better. I went into the office and he was ready to come back to class. As we were leaving the office, the secretary asked me if I had already signed him out to take him home. It took me a second to realize that she thought I was his nanny and that I was there to take him home. I turned around, looked at her and said, "excuse me". She looked at me, recognized me and quickly apologized. "oh, I'm sorry" she said. "I thought you were here to take him home." I replied with "No, I work here. I'm taking him back to class." She didn't say anything and just went back to doing whatever it was she was doing. I kind of just let it slide.
Later that afternoon I arrived at my next session, and as I sat in the car waiting for the security in the booth to open the gate (they live in a gated community), I started coughing. I did the polite thing by coughing into the inside of my elbow and not my hand, seeing how she was about to give me my permit to put in my car. The security lady looked at me and asked me, "are you a cook?" I looked at her at this point kind of pissed. "What?" I asked. "Are you a cook?" she said. I replied angrily, "No, why?" "oh, it's just that I've only seen cooks or people that work with food, cough like that." she said.
I snapped back, "No, I am an educator and I teach my kids to cough like that so they don't spread germs. Is that all?"
She didn't say anything back and just opened the gate for me.
Is it because I'm a female that people assume that I'm a nanny or a cook or whatever it is they think. Or is it because of my race?
Well check this, I am a female, I am a Mexican and on top of that I am a professional. I am smart, I am educated, I have two degrees and I will kick the ass of the next person who asks me if I am some little kids nanny.