Is it normal to be so scared irrationally?

Hi, 18 year old male here. I'll try to keep this relatively short (or at least easy to read), because I know how off-putting huge posts are. Also, it's one of those whiny teenage un-relationship stories you all probably hate, so you might as well stop now if that isn't your thing. Obviously I'd prefer you to keep on reading, but I can't make you. I'll throw any information I think might be at all relevant at you, in the hope that some of it is. Thought you deserved warning!

Basically, I've been in a sort of "flirtationship" with a girl, also 18, since mid-December 2011 (today being very near the start of February 2012). We have also become close as friends. I've been really wanting to ask her out for all this time, but I always get too scared.

All our mutual friends tell me she wants me to ask her out on a date and that she wouldn't reject me, so I know I've not got a fear of rejection. I've never asked a girl out before, or been on a date, or had a girlfriend, or kissed a girl, and so on. I would ask a guy friend for help and advice, but they all have no more/even less experience than me. She has had two or three boyfriends before, none of whom I have ever met, but I believe she is still a virgin.

I know from her best friend, also one of my good friends, that the only reason she doesn't ask me out herself is because of some baggage from her last relationship; however, this doesn't put me off her. I won't bore you with more details about that part because it really isn't important, but don't bother telling me not to go into a relationship with someone with baggage because I won't listen.

Our flirtyness has attracted a lot of attention from people who barely know either of us; it feels as if the whole school is suddenly interested in us. We both get asked about each other by people we barely know on a several-times-daily basis and it can be quite intimidating.

She keeps giving me obvious opportunities to ask her out, dragging me away from everyone else to talk alone and such like, but I either don't spot these until long after or get too scared to act upon my chance. I worry that soon she'll start to give up on me and think I'm not interested after all if I don't ask her soon.

As it is Valentine's in less than 2 weeks now, I really want to ask her out on a date before then. Is it normal to be so scared, despite having no fear of rejection? What do you think my problem might be? Can you give me any handy hints about how I can "man up"?

TL;DR: is it normal that I'm too scared to ask out a girl who I really like, despite knowing she wouldn't reject me?

I think that is just about everything... thanks for bothering to read, if you did! I will respond if you have questions for me. Big thanks in advance; if you give me a helpful answer I will love you forever. I have some reasons in mind myself, but I don't want to limit what advice you might be able to give me.