If you are chilly dipping your chips, that is due to your hands being behind the ball at impact. This might be a clue to your full swing. Look at your ball position again. Be in the middle for the short irons, and a little more forward (1 or 2 balls) for the mids, and 2-3 balls forward for the longs.

Balls that just start right and go right is due to your hands not getting the club face square on the ball. Many reasons for this: Bad Grip, hips/shoulders not getting around, hands not fully releasing/late release.

If your drives improved and now all of a sudden the irons go south, that is usually due to you swing the iron like the wood (low-long takeaway with an upswing). You will want to increase the steepness of the angle of decent on the ball for the irons by taking the club back higher and having a fuller wrist cock. This promotes the hands to be used more before impact and created the steeper angle.