Hi, Kaliya and Hide and welcome to the forum! We need more information because this doesn't appear to be a molting problem. When parrots molt, you do not really see any 'holes' anywhere on the body plumage - you don't even see the down. You might see a rectrix (tail primary feather) or a remige (wing primary feather) missing when they fan fly but it's quickly replaced by the growing pin because in a normal molt, the new forming feather pushes the old feather out so it's just a matter of a couple of days before you see the new one. If you answer the following questions, we will be able to narrow down the cause of the problem... What exactly is his diet - not what you give him but what he actually eats and at what time during the day? And what is his light schedule? Is he flighted? How old is he? How long have you had him? If you adopted him as an adult, does he have a history of FDB?
In the meantime, please stop feeding him egg white or any other animal protein. These birds are strict herbivores and never consume animal protein in the wild but, even if they did, there is not a single species of parrot that has eggs as part of their natural diet. Your reasoning that protein is needed for feather production is 100% correct but all pet parrots eat way too much protein to begin with so more is not what is needed here - it might very well be that he needs less protein.