I'm not sure how you define "hook up". I've seen it used as either hanging around with someone or a euphmism for casual sex.
If you are having casual sex with random girls, then that is obviously not a good idea.
If you are just hanging out with random girls, that is perfectly fine at your age, and in my opinion, is healthy. It will give you experience relating to the opposite sex, and you will learn (hopefully) what qualities you find important in the opposite sex, and what you should look for in a long-term partner when you grow up. Also, as Ellyn says, it is an amazing opportunity to learn about relationships in general, even though, as you already know, they won't last.
I think you feel sad when you are away from this girl because you LIKE her and enjoy the way you feel when she is around. This is normal, and also very sweet.
Relax... I'll need some information first. Just the basic facts - can you show me where it hurts?