Syncing messages after a new phone

With my previous phone, I had my entire iMessage history across all my old iPhones on my phone, but only the history post January 2013 on my MacBook Air. Not sure why, but that was fine.

Yesterday, I had to get a new iPhone. I couldn't do a full backup because there wasn't enough room on my MBA, but I thought I backed up my messages and apps. Turns out that didn't happen. When I restored my phone, iMessages were restored as of the last full backup - September 2014. So now if I want to find something in a message earlier than September 2014, I can only find it on my phone but if I want something September 2014 to mid-August 2015, I can only find it on my MBA.

Is there anyway to get my entire iMessage history on my devices?