Why is home sharing only sharing some of my library?

Hey, everyone. Hopefully you can offer me some advice on what to do here. I have an iPhone 4S, and I have had a laptop for five years that my iPhone has always been synced to. I recently got a new laptop and I was setting it up on Christmas Day a few weeks ago. I was downloading the iTunes software onto this new computer, and I wanted to transfer every last thing from my iTunes library on my old computer onto this new one. I thought I would require a USB drive, until I saw that an easier way to do this is using "Home Sharing". I authorized my computer, and was pleased to see that it worked out just fine. All of my music, movies, podcasts, TV shows, etc., including those that I had not downloaded directly from the iTunes Store, were on my new computer.

Later that day, I updated my phone to iOS 7, since I had not done so yet. During this process, in what I understand is a common error, I was forced to restore my phone and it appeared I had lost ALL of my data. I was obviously disappointed, but somehow (I don't even know how I did it) I backed it up and somehow all of my data came back.

However, my problem is with my iTunes library. Although the Home Sharing option seemed to be working at first, that same day my music library was reduced to only the things that I had bought from the iTunes Store, including songs/videos that I had bought years ago and deleted months ago. Plus, some of the info I had added to some of the songs (accessed by right-clicking on a song, then clicking "Get Info"), including lyrics and such, was gone as well. Play counts were erased too. I may understand that some of the music that I did not get from the iTunes Store would be on this new computer, but what confuses me is why these files where shown as being in my new iTunes library (and the files were accounted for on the computer, they played fine, I tested some of them) and then they vanished. I don't know what I should do here. Tips?