Recover lost messages and contacts after old backup

Hello,

I'm extremely frustrated with myself for doing this, because after doing some research on here I know I kind of messed up, but I could really use some help. I got my first iphone 5s over 2 years ago, and the last back up I did on it was September of 2015. About 3 or 4 weeks ago, I upgraded to an iphone 6s, and at my phone carrier (US Cellular), they transferred all of my information to my new phone, including contacts, my messages, photos, etc.

Last night, I decided to upgrade to iOS 9.3.1, and usually when I do upgrades like this, I plug my iphone into my computer to save memory on my phone for download space. But this was the first time I plugged in my new iphone to my Macbook, and half paying attention as I did it, I had it restore my iphone to the way it was back in September of 2015. So when I opened my phone, all of my apps, messages, and contacts were the same as they were then. I don't want this, particularly because I want my messages and contacts back to the way they were in their most recent form.

Interestingly, I still have all of my recent photos, but my messages and contacts are gone. In addition, my most recent contacts and messages are on my Macbook if that helps with anything. Is there anything I can do to recover these things back on to my iphone without spending $70+ on a third party app to do so? Any help is appreciated, and it would be nice to get this resolved as soon as possible. Thanks!