Is it normal that i felt embarassed

I went for my physical the other day, the doctor is an older man and also a friend to my parents. I have gone to see him before but never for a physical. His nurse also older lady and happens to be a friend of my moms and we see her at church every Sunday. When I got there she had me fill in a health questionnaire, then she called me to the exam room. When I walked in she told me I had to get undressed so I did take my shirt and pants off and was standing there in just my briefs and socks and feeling maybe a little embarrassed. She turned around and looked at me and told me to take my briefs off also and walk over to the scale that she was going to do a weight and height on me. So there I was standing naked in front of her and she walked me to the scale. First she told me to stand on the scale facing the wall and to stand nice and tall with my arms at my side and she took my weight, then she had me step down and told me to get back on the scale with my rear end facing the wall and again to stand nice and tall with arms at my side for my height and she was standing there right in front of me. I did feel embarrassed thinking how she sees me at church every Sunday with my parents. I did think to myself well she is a nurse and this is her job. I did not feel too embarrassed being naked in front of the doctor I guess because he is a guy. The nurse was in the room for my physical. I am glad I am in good health, just over weight and told me I need to stop smoking. He did tell me I needed three shots which the nurse gave me in my rear end and I will say that did hurt I hate needles. I have to go back in a week for a follow up on blood work. When I got home and told my parents about being naked in front of the nurse they told me I should not be. What do you think?