When you say you want to build your back, are you refering to the lower/upper or both? I'm asking because you mentioned deadlifts but not rows or pullups.
I had a major injury to my lower back almost 2 yrs ago.
My goal after and during the injury rehab period was that I wanted to continue working my back and legs. I won't get into legs. For back, I couldn't do bent barbell rows and deadlifts (or any compound exercise that uses the lower back for stability). I could do pullups, which helped my upper back a lot, and can also help to eliminate upper back and shoulder weaknesses and imbalances. For rowing I could do cable rows with light to medium weight without any effect on the injury. Instead of bent rows I did one arm DB rows with the opposite leg from pulling arm on a flat bench. I started on light weight and progressed to using as heavy as possible, I had gone up to 90's. These 3 exercises I did for my upper back.
For my lower back all I did were back extensions. That was pretty much all I could be besides stretch.
This is how I worked on my back with a lower back injury and pain.
I am not saying or recommending you to follow this or jump into the weights head first. I got doctors advice and the Dr.'s advice was avoid any lifts that compress the lumbar spine.
Eventually after a year of doing this my lower back was strong enough to start with light compound movements. I did this to test the waters. Things were good and with a progression I slowly added the following movements into my workouts, in order
Front squats-start of year 1 after injury
Deadlifts-soon after front squats
Cleans-soon after deadlifts
Bent Rows-soon after cleans
Back Squats-2 later
SLDL-a few months after that
Snatches-2 months ago
Overhead squats-2 months ago
It's been nearly 2 years from my injury, after careful assesment and rehab, I am now consistantly going over 80% of my 1rm on all of the compound exercises except the good mornings which were implemented 1 month ago.
Just a rant on my experience with building a back with lower back pain.