Is there any other ways to track an iphone without icloud?

So about two months ago, i lost my brand new iphone 5s (or it was stolen) in the gym at school. I just got it for christmas this year. I looked everywhere i possibly could and it was never found & still isn't. I tried to track it at home but i couldnt without my icloud being set up. So me, not knowing this would effect anything. I got onto my moms iphone, and logged into my apple id on her phone, then set up my icloud from her phone. Once i was done i tried to track it again and it said it was here at the house (cause i was logged onto moms iphone) So that was out of the question. My dad went to verizon and the guy gave us a number to call to track it, so well called and the lady told us there was nothing they could do about it if i logged out of my apple id on my iphone. So That was out of the question too. Is there any other way I or verzon can track my Iphone with out having to use icloud? Or any suggestions on what i should do. If not, if i bought a new iphone 5s would there be any way to transfer all my photos, videos, notes, apps. Etc. From my old phone onto the new one? Anything will help.

Yes, you could set up find my iphone. It will show you the exact location of the phone. Hope this helps.