That's completely normal teen angst and life choice stress. Happens to everyone at times, just make sure you get over it soon enough, and don't fall into a spiral and turn into an emo, or we'd have to shoot you.
You don't know what to do with your life yet, so you don't really know what you're in school for, and you're not motivated. As for life choices, nowadays it's a bitch, because publicly reglated educational systems put every kid into rails towards college, but most don't know what they want in life before they enter college, or even after they graduate.
Of course you will want a college degree if you want a good position later on. Though people are sometimes happier with other occupations, the Army is just the most obvious example. You should do your best at taking a look at actual ways to earn money, and thinking which would you prefer.
I think it may be a grave mistake to choose a degree only because it sounds good, with no idea of how it may translate into any job. You may get lucky and stumble afterwards into a job that you like, but many people that do this end up having to start their lives from scratch after they've spent years graduating.
If you could really like the army, don't worry about being weak, worry about what you can take, because if you endure the training it would make a man out of you haha.
Once you know what you want to do for a living, it will be easy to draw a road map that can hopefully take you there. Even if it's difficult or ambitious, if it's what you really want go for it. If you don't make it in the end, because too many people wanted too little jobs, still anything related that you'll be able to snatch will be better than studying for the heck of it and ending in an unrelated and shitty job. Once you know where are you intending to go, you'll also be more motivated to study and such.
As for the girl, you're making no sense, wake up, snap out of it. :P Leaving her before trying because you're not good enough? If she doesn't like you, you won't get her anyway, and if you get her, it would have been supposed to happen from the start, and she likes you best.
Incidentally I don't think she'll be interested in listening to you for more than two days if everything you have to say is how depressed you feel (unless she's a hardcore emo, and that's just a pose anyway--she won't). If you're too down for prom and that it's a different thing. But come on, you'll only make yourself more depressed if you withdraw attention from life to yourself.