I get this too. Our legs are stronger than our backs. Think a car with an engine that can put out more HP than the transmission can handle.

This winter I've been lazy and sick, but last winter I did see a PT and did a lot of back and core work. You can find a lot of exercises online, such as bird dogs, superman, plank, side plank.
Once the pain decreases deadlifts and squats with free weights are also a huge help for backs.

I find alternating seated and out of the saddle on climbs and sprints helps a lot, gives the back a break.