Give it time, you'll start to miss it when she becomes less clingy.
My boyfriend was like this at the beginning of our relationship, its because he was insecure, and although he denies it I think he still is, to a certain extent. He needs constant confirmation that I still love him, I'm not going to cheat on him...sure its annoying but I love him so I deal with it, I tell him I love him all the time. You're girlfriend is probably the same, because you're her first serious bf and probably thinks if she doesn't act like the good gf she'll lose you.
All of this is speculation until you do mention it to her, nicely, don't even imply that she's clingy unless you want to upset her. Nobody wants to hear that from their first serious partner.