Hey, bud. I'm not an expert in these things, but I may have some insite for you.
I have trained in Shudokan Karate-Do, dabbled in Tae-kwan-do, trained exstensively in Kenjuitsu, and of course what the military taught me in hand-to-hand for the battlefield (kinda like Judo with a knife). Having said all that, I'm about a lifetime away from being a master in any of it.
While on active duty, I sustained an injury that left me with only 30% use of my left arm (yes, I was a lefty, of course)
I had to completely re-train myself to shoot as well as hand to hand techniques.
The first thing you should do is visit some local Dojo's of different arts and respectfully ask to observe a class. Some will let you, some may not. While observing, watch how they execute punches, blocks, and kicks. Determine whether or not your back could take it( I do not know the extent of your injury, but there are some techniques and exercises that will strengthen the muscles of the back) REALLY REALLY study blocking techniques, if they cant hit you, they cant hurt you. Since your injury is to your back, I'd stay away from an art that involves alot of throws or leverage. You may have to modify some techniques because of you injury.
Whichever art you decide on, I'd like you to remember one thing, and others here have eluded to it. It doesnt take 15 years in an art to win a fight. It takes a Warrior's mind. I have seen guys who are extremly knowledgeable in their art and have been practicing for years go down in a fight. The reason is, IMHO, is because they may be outstanding martial artists, but they're not Warriors. A fight is a fast moving, ever- changing thing. Its not Kata. Whichever art you choose, please just make sure that if it comes down to using your skill, make sure it is quick, brutal, decisive, and unquestionably effective. THAT is how to stay alive in a hand to hand battle, again, my humble opinion.
If you'd like to converse more on this subject, please feel free to e-mail me, ok?