OP, my baby did exactly the same thing and he's now one and thriving! Like you, however, it did cause me panic attacks and terrible anxiety at the time. It's so frightening while it's happening.
OK, so first of all, as she did go a bit of funny colour, I'd recommend getting her checked out by a GP. This isn't because I'm concerned (I'm not a health professional), but because if babies have any episodes of turning pale/grey/blue (I don't know how long yours lasted?), it's a routine recommendation to get them checked out. Again, this is not to worry you - it's so your doctor can put your mind at rest!
I'll share my experience, as it sounds like why my DS did. What probably happened is that she swallowed the wrong way and, in response, had what's called a 'vasovagal syncope'. Basically, the shock of having swallowed the wrong way caused her to stop breathing, which caused a drop in blood pressure (hence the funny colour), which caused her to briefly pass out. This is what my doctor explained to me when I got my DS checked out. She was very reassuring. She said it's not uncommon and some babies are more prone to it than others. She said babies DON'T die of it (I asked!). Don't think of it as 'choking' - it's more of a funny response to swallowing the wrong way. I also asked whether swallowing milk the wrong way could lead to actual choking. She said no. She told me that the airway is structured in such a way that even if some milk got into the lungs, he's still be able to breathe well enough for me to have lots of time to get him some medical attention. And she also said I'd know if milk had got into his lungs, as their breathing goes funny. Anyway, my DS never did need any further medical attention and eventually grew out of both the vasovagal syncopes and the swallowing-the-wrong-way.
If she does have another episode, just gently put her upright and rub her to remind her to start breathing again!
I never managed to stop the swallowing-the-wrong way while breastfeeding. We tried feeding more upright, expressing before feeds, pinching the areola, but nothing solved it, other than time! For us, it got a lot better around the 2 month mark. It's definitely worth getting some technical help, though, and seeing if anything does work better for you. We found he coped better with bottles and gave him ebm for a while before transitioning back to the breast.
Anyway, again, I'm not a medical professional, but this was my experience. I hope that helps!