AITA for calling a woman fat?

Hear me out please.

I am a woman in my thirties and I have a daughter in fifth grade. In order to pick up your kid you have to go inside the school and line up outside the classrooms. So when pick her up I make small talk with a lot of the parents while waiting in line.

My daughter has been going to this school since kindergarten and has been friends with the same group of girls. Naturally over the years I’ve become friends with some and friendly with others.

There is one woman, let’s call her Brandy, who has never really been friendly with me, her daughter and mine aren’t very close either. However, Brandy is very close with another mom I consider to be my friend. So I see her around often at birthday parties and such and I’ve always gotten a very mean girl vibe from her.

It’s been warming up where we live and yesterday was the first day that got above 90 degrees. It was hot, so I wore shorts to school pickup. Brandy is a larger woman, there’s no way to sugarcoat it. She’s a big lady. And I am a very pale lady. I do not tan and I don’t bother to try so I have really white legs.

While I was waiting in line, making small talk up walks Brandy. She looks at me and says very loudly and rudely, “Wow, you’re really pale! And started laughing.

Now I know I’m super pale and if she had said it in a joking tone I would have laughed it off. But it was said as an insult, with a very snarky tone that pissed me off. So after a second I said, “Hey, how would you like it if I walked up to you in public and said wow, you’re really fat! And then laughed in your face?” It was rude I know, but my appearance had just been insulted in front of a group of parents at my daughter’s school.

Well, she obviously didn’t like that and got visibly upset so I just turned around and walked towards the classroom because at that point they had started releasing the kids and I didn’t want to be part of a scene.

My friend that I mentioned earlier reached out to me later and said that Brandy was really hurt by my comment and that “calling someone pale isn’t the same as calling them fat because you can change being pale.” I don’t quite understand that line of thinking because being overweight is something you can also change.

I’m being told that I should apologize for calling her fat but I don’t think I should have to since that woman insulted me first.

Am I wrong in feeling this way?