If you changed your alignment so the arrow was to the left of your dominant eye, perhaps by pushing the string hand further into your face, this could cause right misses. This seems somewhat unlikely, although possible, I guess, depending on your facial structure. Mostly people seem to have the opposite problem: their normal side of the face anchor puts the arrow outside the dominant eye causing left misses.
I think the main problem with pushing the string hand hard into the face would be that the sideways force needed to hold the string hand against the face might deflect the arrow on release, or possibly cause the string to hit your face or nose. However, I have seen good shooters who like to plant their string hand firmly against their face. I prefer a light touch of my string hand to my face. You should be able to sight down the full length of the arrow at full draw and imagine the path it will take. If it deflects from that path to the right or left on release, that generally means there was some movement of the release hand other than just relaxing the fingers and letting the string go.