[Erax]

Since you mentioned feeling 'down' in the afternoon, it could just be your daily cycle. Sun Tzu wrote something about the army being ready to fight in the morning and useless by nightfall, so it's nothing new.

Regular physical activity will give you an extra 'zip' which Lasts the whole day, even during the down-part of your cycle (that's what's so great about it, you'll feel better even when not exercising).

Improving some aspect of your situation (making some friends, for example) will reduce frustration and help fight depression.

About the girl... you said she is a very social person, but I get the feeling she isn't dating anyone else. When you feel you are ready, you could begin by asking her just that - 'You have so many friends, how come you aren't dating anyone ?' It's a classic line, it gives her a pretty good idea of your intentions but it doesn't commit you to anything, and her answer will help you decide what to do next.