Can a half-boiled egg be fed to a baby less than a year?

Can a half-boiled egg be fed to a baby less than a year?
I got the answer through my own experience myself.
The other day (2 months back), without doing so much thinking, when my hubby asked can he feed our 8-month-old baby Hanie a soft-boiled egg while we were in a restaurant, i said "i guess so" which was a very very wrong answer.
Couple hours after that, hanie was throwing up so bad, almost like an adult throwed up, made me wonder where those liquids coming from..i'd say, a lot! how could a very tiny stomach can contain that amount of liquid. It was a multiple series, almost 7 times. i had to change her clothes (so did mine) again and again...10 to 15 minutes apart. after the seventh series, she looked so tired and slept right after she throwed up. i felt so bad.. this is one of the moments where i felt like i failed as a mother.. :(
An article i found regarding eggs and allergy :
Introducing Eggs - When Can I Give My Baby Eggs?
An egg allergy occurs when your baby's immune system overreacts to the protein found in eggs. To be more precise, it's the protein found in the egg white.

Start with Egg Yolks
What this means is that you can introduce an egg yolk before an egg white, beginning at around 6 months of age. They're quite nutritious, too. A 2002 study in the American Journal of Clinical Nutrition showed that egg yolks can increase iron levels in babies 6-12 months of age and that eggs fortified with Omega-3 fatty acids also help increase DHA levels in the same age range. Both of these findings are a bonus for babies who are starting to lose their own iron stores or who might have to be weaned from breast milk at this age.
While you can separate the yolk from the white before cooking, this can sometimes leave bits of egg white behind. Even a little bit of the the protein can cause a reaction. The best way to separate the egg is to cook it first by hard boiling. Then you can carefully peel off the egg white (use it in your own tuna salad or other salad) and mash the yolk with a fork. To get a smoother consistency, add breast milk, formula or water a little at a time while you mash.
Introduce Egg Whites Later
For families that have no history of allergies or related illnesses like eczema or asthma, egg whites can be introduced starting at 1 year of age. For families with a history of these illnesses, The American Academy of Pediatrics says it's best to wait to introduce eggs until your child is 2 years of age.
Whether or not you have a history, the first time you introduce eggs, be sure to watch for the signs of an allergic reaction (hives, difficulty breathing or asthma symptoms, swelling of the mouth or throat, vomiting or diarrhea and loss of consciousness), know how to respond and be ready to call 9-1-1 immediately.
please note that : hard boiled egg (not soft-boiled egg, like i gave to hanie. no wonder she throwed up badly. it wasnt a fully cooked meal!)
Alhamdulillah, she recovered fast. After the last session of throwing up (8th times in a middle of sleep), she felt asleep..very weakly. after 10 minutes or so, i woke her up and fed her. Luckily she accepted it and fell asleep after feeling full. I was afraid that she dehydrated. But Thank God, everything went okay the next day.
The experience really made me be extra extra cautious when it comes to food.