I'm left eye dominant and shoot long guns from the right side, never has mattered before so I doubt that's your problem. With a pistol I do fudge over and use the left eye.
Really sounds like something could be loose. Too bad you're having trouble finding someone else to test it. That's the best test. Or you could borrow a scope or red dot but then that wouldn't test your irons.
The biggest issue with assembling an AR isn't so much getting the parts together right - it's getting the right parts together.
US Army 1966-69, VFW Life Member, Retired Geek