Trying to transfer music from iPhone to new computer, missing files?

So I have a hard drive backed up with everything on my (now broken/unusable) computer before I bought a new one.
I just manually transferred all of my iTunes media into the new iTunes, but for some reason I'm missing over 100 items when I compare the song amount on my iPhone?

Is there any way to transfer the music from iphone to itunes, or be able to check which songs were not transferred? (I have thousands of songs)

I tried AnyTrans but the trial only allows 50 songs a day. Hoping to not have to shell out cash for a program lol.

Dff