Yes, I think it is possible to acquire this later in life. I would recommend to make a test at the doctor's, and - in case there IS an allergy - to ask him about the options you have to deal with it. I wouldn't give up my furkids either - no way!

Years ago I have been diagnosed being allergic to cats but I did not accept it - funny thing is that I got rid of it that way.

Good luck!

Kirsten