NO WAY! imo.
you are dealing with IGE allergy, so this has to be done carefully under medical supervision. EXPOSURE is NOT the way to overcome ige allergies, not after allergy has been established.
if he is reacting to cooked egg, he is still allergic to all forms of egg. normally if skin prick test or rast/blood test to cooked egg allergy idicates outgrown, thats one thing to try, ( we were lucky we did a controlled test for cooked egg in a hosptial ward , with a nurse on standby, my son was 7yrs at the time.) for raw egg allergy, again that depends on testing for the raw egg.
my son has failed his food challenges over the years and we are very grateful that each was done in a hosptial setting. however this is due only to the fact that we live in a area that meant we could be reffered to a london allergy clinic.
give piriton to your child after ANY egg exposure if he reacts, dont hang around waiting.
I think you should ring the anaphylaxis campaign helpline for advice, i think you need to ask for the nearest pead immunologist to you or a part time nhs clinic run by one. (allergyuk can help as well)
I suspect they will advise you to stop giving your child egg. and use antihistamine.
they will also suggest that your child might need further testing as he grows older, for instance peanut allergy and egg allergy seem to go hand in hand in the early years of an allergic childs life.
egg still can be outgrown, but this does take time and is indvidual and ige reactions can be different every time, and can be severe.
other factors that may need care are for ezcema and asthma, esp the latter as that is a huge factor in food allergies.
your instinct as a mother means alarm bells are ringing. listen to them, your're spot on.
good luck.