I will say that it is quite rare for someone to develop a food allergy later in life after being exposed to that food many times without a reaction. With that said it is possible for you to develop an allergy as our immune system evolves over time. It just isn't that common. There are two reasons why you should get this checked out. First, egg allergies are common and have implications for getting shots every year such as the flu shot
(which contains egg products). The second reason that you should get this checked out is that your apparent reaction sounds severe. You never want to ignore a reaction that could close your airway and prevent you from being able to breath.
I suggest that you schedule an appointment with an allergist. The reason I want you to see a specialist is that you need allergy testing. This is where the doctor
will challenge you with a sample of the allergen (usually with a small injection under the skin) and see if you react to it. If you do, then you will know that you are allergic to eggs. If you don't react to it, then you know that the feeling of your throat closing was caused by something else.