Do you think having an african grey parrot is bad for my asthma?

Not necessarily : The usual animal allergy is to fur bearing mammals (cats and dogs). However, we can become allergic to almost anything and its this allergic response than can trigger an asthma attack.

Avoid if triggers sx: There is a condition called Hypersensitivity pneumonitis or HP which is an immune reaction to a variety of agents, including bird feathers and droppings. It is distinct from asthma, and if you have asthma symptoms while cleaning the cage or while near the parrot, then I would suggest avoiding this possible trigger.