Can you get allergic to cats when you get older?

yes you can, You can develop an allergy to something at any point in time in your life, I used to be allergic to chocolate now i am not, I used to be able to eat tree nuts ,now I am severely allergic to them! Mom mom was never allergic to cats and now she is. They can come and go

Yes, allergies start when your immune system miss-identifies something entering your system, so you can develop allergies at all ages. Same with sensitivities(which is more what this sounds like, because true allergies kill), you can develop 'em at any time, and luckily, you can also overcome them at any time, because if you're exposed over time, your immune system will relax when it notices, it's not a deadly invasion.