Exercise to strengthen my back?

Can you:

Deadlift?
BB row?
Do pullups?

There is heaps of options, but it really depends on what you can/cant do. is your injury prevent anything now?

If you are "healed" then the above wont hurt you again with proper form.

When i added 1 arm Dumbell rows to my routine, my back pain was erased, if that is anything to go by.

My back is also pretty strong overall. I do all of the above.

Have you seen a sports physio?

I have suffered from chronic back problems for years. This is the solutions I have found. Yoga to increase flexibility if you have an android phone there are some free apps called daily yoga for back/abs/hips etc they are all ten min routines and I found IMMEDIATE relief. The increase in flexibility alters the tilt of your pelvis and takes the pressure off the disks. Do any exercises that strengthen your abs to take the pressure off your back increase the strength in your glutes and hips. All these oh and Pilates has a lot of routines that will also build up the muscles in your lower back and abs. And once the pain is gone and you feel you have reached a level of strenth where you no longer feel your back is weak you can work into some weight training like dead lifts etc

I had myself a herniated disk, and a bulging one at the ripe old age of 21.
Once I could comfortably stand up and move around, I started ab exercises. Gentle crunches, mostly.
And an exercise for my back which involved lying on my stomach with my toes/feet anchored, putting my hands on the floor at my chest (push up position) and then arching my back and pulling my chest off the floor, using my hands to support my weight if needed.
Eventually work up to not having to use your hands at all.
The work on obliques (that twisting motion).

Yoga is awesome, and so is Pilates.
Remember that your abs are equally important as your back muscles in stabilizing your spine.

Avoid running, and other high impact exercises. Slow, intentional movement is the safest bet at the beginning.

You can do it! I am totally recovered.