Are you allergic to Pets?

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I once brought home a cat from a neighbouring shop so that i can keep it as my pet. I brought it home but every time i went close to it i would just simply start sneezing. Later i found out that i had allergy to cats. So instead of a cat i brought a puppy but same problem here. It was then that i knew that im allergic to pets only. Does anyone share any similar problems?