Does your horse's bridle fit correctly? Here with advice on how to check the fit is SMS Qualified Saddle Fitter Diana Fisher.
With your horse's headpiece, you need to make sure that there isn't any tightness at the TMJ joint and that the browband is big enough so that it doesn't pull the bridle forward over your horse's ears.
For your horse's cheekpieces, ideally you need the buckle of the cheekpiece to be in line with your horse's eye. To do that, you may need to change your horses's cheekpiece to a shorter one.
With your horse's noseband, you should check that it falls beneath your horse's cheekbone, to avoid rubbing. Having a finger to a finger-and-a-half distance between the bottom of the horse's cheekbone and the horse's nose band is a good measure to avoid this.