You might want to shorten your running distance, but increase your speed. Long jogging sessions can cause wear & tear on the body. And especially if you're not giving your body enough rest in between this could be making your back worse. I used to run 3 miles every day, and although my endurance was great, I was living with pain every day. Much later I shifted my focus to weight training, high-intensity interval training, sprinting, etc and I felt better overall.
As for strengthening the lower back, there are a couple exercises I'd suggest. The key thing to remember is to ease your way into this since your back may be suspect. So start very light. In fact, you may want to give your back a rest and wait until it's feeling better before even beginning these.
- Stiff legged dead lifts - This exercise is a little simpler to master than the conventional dead lift and focuses primarily on the back and hamstrings.
- Hack squats - Hack squats are a little more awkward to get the hang of. But they'll target the legs and the back. And unlike any over the shoulder squat, you don't need a squat rack to do them.
They use a barbell in both of these videos, but they could just as easily be done with dumbbells. There are actually a lot of muscles being worked between these two exercises. Even your shoulders and upper back will get a bit of a workout. They are great lifts to do. But again, start light, and gradually increase weight.
In addition to this, it's always a good idea to work the opposing muscles. So you should be doing situps or crunches as well. In fact, I've found that strengthening the abdominal muscles is just as important as the back muscles to prevent back pain.