Assuming your arrows are correctly spined and your bow is within its specs, and your form is good, etc.,
Great start.
Question.....based on the advice above. I'm trying to think of what I would do if this were occurring with my setup.
Why wouldn't you corrct the flight of the arrow, first (i.e. make sure the arrow is flying "true") and then make a simple sight adjustment? I suppose I'm trying to figure out why where your arrow was impacting mattered......if your flight was still erratic (side to side). Once your arrow was flying ture.....it would seem like a simple sight adjustment would have all problems solved.
Wouldn't you want to make your center shot adjustments first (again....assuming the above, quoted was a given)?