Don't pursue her romantically. If she's with someone else, leave it. Don't be that guy.
Like others have said, give it time. You said yourself when you weren't around her you were fine, and it was only seeing her again which stirred the feelings up. Maybe this girl you're going out on a date with isn't the one, but you'll find someone in the end and then when you see your friend again you'll just be happy to see her instead of pining for her.
I think some people need to step away from the Meg Ryan boxsets and realise that people of different sixes can be friends without there being a romantic undertone involved. She's clearly capable of pursuing a romantic interest, and as harsh as this is, it wasn't you, OP. But there will be others - trust me.

The most rational post in this thread so far.
It seems like almost everyone goes to 2 extremes; either chase her, or run from her. I don't think either situation "works". As corny as it sounds, acceptance, I find, is the best solution. If you truly want this girl to be happy, then you should be happy that she is happy being with someone who makes her happy. So it isn't you, yeah it kind of svcks, but it isn't that big of a deal in the grand scheme. The intense feelings you have are just a combination of lust and platonic friendship. The recipe for love, but also the recipe for heartache. So move on from the lust, and leave only friendship behind. It might svck a bit every time you run into her, but there are more important things to focus on. The better you get at understanding these feelings, the more it will make sense in your heart, and the less tumultuous it will be on you.
You sound young, and we've all pretty much been where you are. One thing I feel like a lot of people focus on is having to "be" with someone. Feeling this need to be attached to a partner. One of the cold realities of this world, is that you are always "alone". This is different from loneliness, however. Don't strive to not be alone, you will never truly achieve this, only you can make yourself whole. This might not be something you realize until you've had enough time to experience both sides of the coin, but hopefully this will give you something to ponder at least. Don't stress too much about being single, and don't let someone become an object to solve all of your abject situations. Good luck, you'll get past this in time :turned: