Are they actually two separate organs or is it just one that developed differently?

Speaking as someone with a almost-but-not-quite similar story, I regret not saying something to this day 20 years later.

Write down your number, and tell her straight up, "The other week, I assumed my friend had put you up to it and had a knee jerk reaction, but if you’re actually interested here’s my number".
Minimal interaction for minimal anxiety, you can even walk away and see what she does after - if she messages you you’ll get her number then, so you don’t even need to ask for it.

If she refuses, that might be embarrassing in the short term but you’ll forget about it soon. But regrets can last much much longer.