The S&W you're shooting isn't the easiest gun to shoot well, and folks complain a lot about the triggers. But they can be accurate guns.
If it's the gun and NOT YOU, you can move the rear sight a bit to the right and the front sight a bit to the left. While both sights will be off the centerline, it won't look as AWKWARD as is now seems from your description.
If you find that it's NOT YOU (i.e., it is the gun), you should call S&W customer service and talk to them about what's going on.
You shouldn't have to adjust the sights THAT MUCH if you're doing things right. They may want you to return the gun, and you might be able to talk them into working on the trigger while its there. (I've read that several folks have been told to send their gun back to S&W and nearly all of them have been really pleased with their gun after S&W worked on it; there was no charge for the trigger work.
Before you do that, however, you should try shooting from a rest as was suggested in an earlier response. If it's you and not the gun, you'll be really frustrated if the gun still doesn't shoot right for you after it comes back.
Shooting from a rest can be as easy as sitting down at a table or bench at the range, with the gun in your hands and your hands resting on a pad (or a bag of dried rice or beans, a gun rest, etc.). Then aim as you SLOWLY squeeze off the rounds. That take some of the human factor out of the process and you're able to focus on the trigger more easily.
It's important that you use the right part of your trigger finger -- the pad of that end of the trigger finger, or a little closer to the first joint from the end -- but not the joint. And shoot slowly.
The idea is
press the trigger straight to the rear. Too little or too much finger on the trigger makes that hard to do.
- Too little finger on the trigger can apply pressure to the right side of the trigger, pushing the gun to the left as your press the trigger.
- Too much finger on the trigger (maybe the second joint from the tip) can cause you to push the gun to the left, too. Unhappily, too much finger can also cause you to pull the gun to the right, as well -- it all depends on how your finger moves as you move the trigger.
- Squeezing all the fingers of your gun hand as you pull the trigger can also push things to the left.
- Anticipating recoil can do that, too (i.e., unconsciously pushing forward as you pull the trigger)