i agree with furrytail. maybe you're not really looking for a girlfriend. What you need is someone to comfort you, to share you buts and ifs...to ask about what went wrong and who's to blame. a girlfriend is not the right person to have at this time since it will be so unfair for the both of you.
Also "recovering from a borken heart" is not the right term when you are in a new relationship. When we say recovering, even as a child, you'll have an impression that you're still weak due to an illness andthat you are still not allowed to go out and play.
its the same as with a relationship. Maybe the best thing to do is to try to lick your own wound. try to have a short vacation for you to have some space to think it over. A place where nothing can remind you of your former girlfriend. i know it would be hard and it'll take a long time, but that's the way it goes.
how are you and your current girlfriend doing now? girls love sex, for some (including me) its my way of being comfortable with a guy. if i want to know the man that i love deeply, i'll make love with him. And gosh...we make love for the sake of making love. and if you call it "hornyness" too bad for us. But i think that's what your girl wants.. to know you better as a person.
if you want to bring out the seriousness out of her, try to bring her to some place where you and her can talk, like a coffee shop or a park where you can share your future together (maybe a park with family playing together scenery). this could trigger her share her ideas with you. And mind you if she can't stop mentioning your name in whatever topic you talk about.....i can say she's so into you.
Just be true to yourself friend..
again..
recovering goes in 2 ways. either you find a way to help yourself heal your wound, or you let your wound take over you and later on become another disease...hahahahhaa
Goodluck on your healing process friend,
Sincerely yours,
guinevere