Yes! So how you develop an allergy is...you have to be exposed to it first. The first time around you might not and probably will not have a reaction because your body doesn't have those histamines then the second time around you have the histamines and your body fights it knows what to do with it if that makes sense 

My sister in law explained it to me this way. Most allergies have like a cup in your body, it could be a large cup or small cup. Once the cup fills, your body can't take anymore without having a reaction. Her son is allergic to tree nuts, he used to eat them but now gets very sick. He filled his fictional cup eating them before and now he can't fit anymore in the cup, so he gets sick. 

As everyone else said, yes. I took penicillin as a kid then got an allergic reaction to it around age 10 or 12. Since that's a major antibiotic I started taking the next most popular called Sulfa and then developed an allergy to that.

Yes! That happen to me. I took penicillin tons of times growing up and in my teenage years became allergic to it. Broke out in hives and had to go back to the doctor. Doctor said it's pretty common. Hope this helps ;-)

Yes. 

Yes its possible.