I felt exactly the same way about it when I was 15. I think most of my friends did, too. Except the ones who were eager to get pregnant. They were into it. But most of my friends, at 15, weren't interested. The very worst was if our mothers started talking about their own personal experiences, especially if they were talking about us being born.
I reached adulthood with normal psychosexual development, no hang-ups, phobias or neuroses in that area. I'm still not keen on birth scenes or hearing every detail of a woman's delivery, but giving birth is just about the most dramatic and heroic thing that happens in a woman's life. Women, like your mother's friend, talking about all the details with another woman is like two guys who've been in war together talking about battles they were in.
One of the problems these days is TV shows and movies keep going for more and more realistic depictions of everything, including sex and birth. Also violence, but I don't want to put that in the same sentence as the others. I think, actually, it's purposely meant to make people feel emotion. With you it's embarrassment, with some it's sweet sentiment, and I know a few people who've had bad experiences who can't watch at all. It's too realistic.
So, no, I don't think there's anything at all odd about a 15 year old who squirms when birth depictions get a little too real. I think you're pretty normal.