Перевод - Шведский-Русский - Jag är mycket allergisk mot ägg.

I've kept the capital letters in the word "eggs" (яйца), but I'm not sure if you also want the letter "А" of "аллергия" to be capitalised. Also, in Russian is more natural to use an imperative (literally translated as "Please make sure there are no eggs…"), but if you want a more precise translation, the second part of the text can be converted to "Вы можете, пожалуйста, убедиться, что в ингредиентах нет яиц, яичных белков или яичных желтков?", keeping the interrogative sentence and the question mark at the end.