(Info: I had to delete 2 of your threads, as you had 3 times created the same thread - so i cleaned this up to only this one here)
Scott already gave you a good advice here.
Depending on 'how long' you already work out, it can also take time until both bodysides start to even out and become more close to one another.
With having had an injury (i can tell from myself - hence i have a partial rip in my left pectoralis muscle, and a slight twist in my spine) you need to pay really close attention to 'perfect form'.
Always make sure that you have a mind-muscle connection to all in the exercise involved muscles. (good way to get that connection is in the warmup sets)
And then try to 'mentally' activate all of them the same way. To have your brain focused on the involved muscles helps a lot... and will prevent one important thing from happening:
false rewired movement pattern.
You need to know, that our bodies are absolute masters in adaption to whatever problem we have. So i.e. if we hurt our left leg, we 'hobble' and shift things to the right. But this can happen also way more 'subtile' especially with things like a calming down injury or not so obvious stuff.. and your brain will begin to recrute the region of issue differently from the rest, which can lead to a fairly big area of influence, since our bodies are build on a kinetic chain (spine/skeleton). Which is also why just the fact that your shoulder was hurt can even influence areas down into your lats or even further.
On top of that comes the fact - as you discovered already too - that we are not 100 % symetrical either.
So don't make the mistake to treat the 'broken' side more extreme to make it 'cope'. Try in fact to treat it as your main indicator. Meaning do everything with that side first, and then do the same amount of reps on your other side.
Pay attention to form, muscle activation / recruitement (as said above).
And give it time, it can take a while until it starts to even out.
If your latissimus dorsi is quite visibly bigger on the right site, maybe have a check at an orthopaedic doctor / physician. Maybe you have a slight scoliosis too (spine bend / twist) as i have that issue too and that can be a sign for it. It can make your ripcage pertrude a tad more on one side on the back, or having muscles on one side of the bend/twist being recruited differently/stronger to even out the imbalances that the spine is producing due to its misalignment.
Cheers!