Is it possible to completely outgrow an allergy?

When I was a kid I was deathly allergic to cats. I had breathing troubles even if they were in a separate room. After a year long regimen of allergy shots when I was about 10, all of my allergies lessened in severity overall. Since then, I have been able to be in houses with cats without issue, even hold and play with them with no visible side effects. While these exposures are generally brief, is it possible that my allergy to cats is completely gone? I'm going to be moving out on my own soon, could I get a cat as a pet, or could I revert to old allergies if I had constant exposure?