Toddler hates people

My daughter (28 mo) is lovely. She has a great relationship with every member of our small family. But she clearly dislikes other kids and other people. She actually says “I don’t like babies” “I only want to go if it’s empty”, “I don’t like people”, “I don’t want friends”, stuff like that. She would scream “GO AWAY” if she was playing and another child entered the space. She stopped doing it because I insisted it’s not polite and I wouldn’t allow it, but she still cries, go away and seems kind of scared of other children.
We have no problem going to malls, the market or doing errands with lots of people around. She does gets overwhelmed if it takes too long in a crowded and noisy space but so do I.
However, if she’s in a play space she gets absolutely distraught over any other child.

She’s not in daycare yet and we don’t have other kids in our family. But we do live in a place with lots of kids her age, and I try to get her to tolerate them, but it drains me so much. Until 1.5yo she would stop whatever she was doing and just observe the other child. It was a bit strange, but harmless. After that, she decided she didn’t like what she was seeing I guess. It doesn’t look like something temporary because she’s almost 2.5 so it’s been a year.

Her pediatrician said it’s normal, but I don’t see any other kids like her.

Any advice? Maybe people going through something similar?