Possible, yes. Not likely though with most things if you have them regularly - your body kind of recognises it as something that isn’t a threat.
I’m of the opinion that more often than not allergies are your body reacting to the wrong thing. Take seafood allergies for example. The first time your face swells up and gets itchy after eating seafood isn’t the time you had bad seafood - that happened the time before. When you ate the bad seafood, your body reacted and got over it with minor fuss. However, it then tags seafood as the cause of what happened, and the next time you eat seafood you have an allergic reaction.
It is also sometimes possible to overcome allergies, although this is incredibly difficult.