Trouble with iTunes Authorization on iPhone and Mac

I recently got a new Macbook Pro for Christmas, and I moved all of the music from my iTunes library on my iPhone onto my new computer at that time. Since then, they have not been synchronized, and I don't know why. When I download a new song, it will go into my Mac's iTunes library, but it won't sync into my iPhone's iTunes library.

Another problem that seems to go along with the one I described above is that I am unable to listen to some of my songs on my Mac. When I plug my iPhone into my Mac, or try to listen to these songs, I am given the message, "This computer is not authorized to play '*Insert song*'. Would you like to authorize it?" My Mac IS authorized with my correct apple id, but trying to play these songs only allows me to attempt to authorize my computer with an email I have no access to, I didn't create, and I have never even seen before.

I have no way of getting these songs to play or getting my iTunes libraries to actually synchronize on both devices.

Do you think I could maybe deactivate the computer, remove all of the music, and then try it all again? I was too afraid to do this because I'm not sure if there are rules on how often you can authorize a device with the same apple ID.

I am so sorry that this entry is confusing. If you have any ideas at all, I'd be happy to answer any questions you have to clear up some of the details. Any and all help will be appreciated.

Thank you so much!!