I put a back-up for my iPhone on a new iTunes library. Am I safe to sync it now?

I also used TouchCopy to transfer all of my music from my iPhone to the new library so none of it is lost. I'm just afraid that I will lose everything else, including my photos, app content data, contacts and things like that. Will I just have to restore my iPhone to the back-up, and since all my music is there, I will be able to sync it normally without losing any information or content? Sorry, this is my first time doing this.