"increase aeration" just means to increase the amount of dissolved oxygen in the water. As this happens where the water meets the air, increasing surface area, eg by using something which causes ripples on the surface, will cause more oxygen to dissolve into the water. So, a higher filter flow rate, or using an air-pump will help.
Lots of water changes will help as this will cause the ammonia, nitrite and nitrate to be diluted in the clean water.
If your fish spend a bit of time "mouth wrestling" (if they do, you'll know what that is!!!) then this might explain the marks starting around their lips - basically they'd be bruises. If this was the case, you should find they will settle to some extent as a pecking order is established; however parrots are aggressive enough that there will always be some fighting, particularly in a tank of the size you have.
However, I do think it's most likely to be due to the toxic water they're in.