I think you are going to have to be cruel to be kind!
if he is eating the egg then it is obviously not an interternal of dental problem as he can chew, digest, poop! etc
he is just being fussy i am afraid (cats are known for it) as for the cow milk issues i know people think cats and milk go together but they don't, please listen, he only needs fresh water ALWAYs available, even if he is on wet food.
pick one "complete" dry kitten food (complete so he gets all the vitamins, etc that he needs) and leave it down for him, if he get NOTHING else he WILL eat.
Chestnut Cat Sanctuary and Rescue:
It is essential to get them eating complete dried foods [only] as soon as possible - a cat needs 30% protein, not available in any tinned/sachet food. For the first two weeks, mix tin and dried food together [if the cat was not already on dried food when it leaves the sanctuary], slowly removing a half teaspoonful of tinned food every few days and increasing the dried food, until 2 months later the cat is eating only dried food. Not only is it cheaper for you, but doesn�t go off in the summer, and is far healthier for the cat!
Kittens will need feeding 3 times a day with a higher protein (35%) kitten biscuit & kitten tinned food in the early days until they are eating only complete dried foods.
Milk is NOT suitable for a cat's stomach!, Only special cat milk from your pet store. A bowl of water is essential at all times, particularly with dried foods.
please have a look at the following site, it is the cats protection and there is to much info for me to even begin to put it in here!
http://www.cats.org.uk/catcare/leaflets.asp#pr actical