I would play safe and not give your child any form of egg at all.
I also would sugest that you seek a referal to an immunologist before you even try to give egg to your child as a food trial.
Dashing to a GP surgery if your child is having a severe reaction is a total NO NO
For one they wont have the breathing equipment or epi -pens on hand.
If there is a strong possibility that this is classic IGE reaction, rather than intolerance , home food trials are risky.
Its worth researching food allergy, a good book is the 'complete guide to food intolrance and food allergy.' by jonathan brostoff , and published by gamlin.
By far the vast majority of children under 5 grow out of their egg allergy, however, some take years to grow out of it, or not at all.
Its perfectly normal to react to all egg at a young age , and then slowly tolerate highly cooked egg in small amounts. Then grow out of raw egg a few years later.
For some, egg allergy is a life time allergy.
Egg allergy with children often goes in hand with peanut allergy. It seems that the protein structure is similar, hence that some children can eat high heat treated egg, but not raw.
From studies and information I have gathered from the allergy charites, repeated exposure to a allergen does not mean swifter reactions ( this rule is different with regard to kiwi fruit allergy BTW) , the vast majority of allergic reactions that go onwards to anaphylactic are dependent on other major factors, health , other allergies , stress, and asthma management at the time of reaction or accidental ingestion.
It is perfectly possible to have a delayed reaction , some hours later, this is called a bi-phasic reaction, and can be swift to turn in to full blown anaphylaxis , this again is another reason to push for proper medical advice.
There has also been research over the years that indicates that the quicker a young baby or child has antihistamine given ( piriton over 1 yr) as soon as reaction starts the better, and quicker the recovery.
However daily doses of old generation antihistamine ( piriton ) is sometimes considered unhelpful, as it may 'mask' early symtoms, which may re-surfice later on.
For that reason , second generation antihistamies are more suitable, if environmental allergies are troublesome.
However this is more likely to be required as the child is growing out of baby hood, when ezcema starts to improve and they follow the so called 'allergic march'
However , this may be outdated info as my son is now 11 yrs old and times change.
Be aware that food allergies dont come in ones, be open minded and hopeful about the future, for instance 20% of children do grow out of peanut allergy and the rate of outgrowing egg allergy is far higher.
I hope this is useful to you .
My son has outgrown his egg allergy and tree nut allergies, his current allergies are
peanut
all beans
yeast extract ( unheated /rare one this )
tree pollen
kiwi fruit
dog
cat
dustmite
hay fever