First thing I would do is try to shoot from a rest. If shooting from a rest yields POI on POA, then it is how you are pulling the trigger. Otherwise, the sights need adjusting.
Like you, I have found that with the shield and with the M&P 9FS, a slow squeeze of the trigger puts my shots left as well. I can't slowly squeeze it like a DA revolver. I *think* it has to do with how much the trigger travels after the shot breaks. So, don't jerk the trigger. Rather, do a quick/forceful squeeze. And it doesn't even need to be that quick. It has to be more like a determined squeeze. Like, the difference between a slow stroll (slow squeeze) vs someone walking to work, but not rushed (quick squeeze).
Like you, I have found that with the shield and with the M&P 9FS, a slow squeeze of the trigger puts my shots left as well. I can't slowly squeeze it like a DA revolver. I *think* it has to do with how much the trigger travels after the shot breaks. So, don't jerk the trigger. Rather, do a quick/forceful squeeze. And it doesn't even need to be that quick. It has to be more like a determined squeeze. Like, the difference between a slow stroll (slow squeeze) vs someone walking to work, but not rushed (quick squeeze).
I am pretty sure that the factory trigger was too stiff for my pull, and I was pulling left before having the lighter trigger installed. 
