Losing data

First, thank you for those who will provide direction. I bought a new phone and attempted to transfer my pics to from my SE phone to my new phone. I followed the procedures but instead of transferring files from the SE to the new PHONE, the data from the new PHONE moved to the old phone which over ride the existing files. These files in the old phone didn't flow though my icloud account as I have reached my limit. So my help item from those experts out there is, can I still retrieve those data from that old phone? is there a retrieval or reversing action? thanks