First, I'm sorry that you got hurt.... That sounds like a horrible injury. :(
Re: your medication questions.... "addiction" is a word that is usually not defined properly... or, rather, is hard for many to understand in relation to legitimate pain issues. There are very few people w/ chronic pain that are "addicted" to their medication.... But, yes, our bodies do become dependent on the meds - meaning, if we just quit them "cold turkey" - there would be some level of side effects.
So - I think your question is more - will your body become "dependent" on these medications, if you take them as directed, for your recovery time? (You can tell me if I'm wrong and not understanding your question!)
Everyone is different - and this is something I would advise you to talk to your doctor about. *Usually* what happens w/ an injury such as yours.... is a doctor will taper you down on your meds as your situation improves. That way - your body is getting used to less and less medication, as the pain improves. And, hopefully - you'll heal to the point where you don't need medication.
I sure hope you heal quickly.... take care of yourself..... --Tina