The problem appeared randomly and not after an update or reset. The phone in question is an iPhone 6 running iOS 9.2.
The good news is that there’s a pretty easy solution that worked on my phone and here it is. A quick search showed this problem has been plaguing users since iOS 8.1 with no solution in sight and no acknowledgement from Apple that this was a genuine problem. As soon as I would select the photo, the Messages app would freeze.
Another error I kept encountering was that I was unable to send photos over iMessages. The photos I took via the Camera app appeared as little thumbnails in the app but when I switched to the Photos app they weren’t there. A few days ago, my iPhone randomly stopped saving photos to the Photos app.