I've had a few issues with my back recently, with one little tweak getting better just as another one kicks in, to get better just as another muscle goes 'ping' on the other side. This isn't unusual - in compensating for one area of discomfort, another area gets tight or out of balance, and what started as a singular acute injury can become a chain of chronic annoyances.
What's really annoying is that it often happens in the most mundane of movements - I recently had my left lat muscle pull just from pouring milk onto my cereal. This is because, unlike during exercise, you're not really paying attention to what you're doing and aren't braced in the same way. Suddenly, the smallest irregular movement (even without weight) can cause as much damage as the biggest, heaviest squat.
One interesting thing I kept coming across when looking into this a bit was the idea of 360 degree breathing. The idea that, when you breathe in, you should feel pressure going into your sides and back as much as your belly. Try it - put your hands on your sides, under your ribs, and then breathe in and imagine pushing those hands out away from you. Do the same thing with your hands on your back either side of your spine, and then with your hands on your belly button. Now try and do them all at the same time. This should have the effect of bracing your core and spine in a way that feels strong and, personally, quite satisfying. I also found it got a nice bit of stretch and mobility going in my lumbar spine, where I'm quite tight.
If you can get into the habit of breathing this way, in theory you'll be a lot better braced for movements and hopefully avoid some of those back tweaks I've been experiencing. You can see an example of this in the video below from Dr. Sean McBride (just watch up to about the 2:30 mark).