I think that you need to decide your life on what you feel comfortable with and what you think, not what other people think. It's your life, not theirs. It's so nice that your mom is involved in your life and shows concern for your health. I think it's great that you and your mom are still so comfortable and close to each other to be able to do something like that together. Kudos to you!

my son is 13 years old and i go to the doctors with him. i have a big problem with needles, so i have to leave the room (feel weak, get panic attacks). if he wanted me to leave the room, i would!!!
if he was 15 years old i would let him go to the doctors by himself.
i try not to baby my son b/c he is the only child.
looking at the situation on another angle, you have to understand you are your mother's baby, and you always will be. we tend to have a problem with letting go.
talk to her and tell her what your comfortable with.