I moved into a apartmnt a few months ago and noticed they have build up black mold located in the shower can that cause chronic upper respitry inftcns?

Possibly. Mold and fungus can cause chronic infections, but given that you can see it, then use a bleach solution to sterilize it.
Perhaps. Generally this type ofmoldcan be treated effectively with a diluted beach solution and a little elbow grease. Once the mold is removed things shouldne fine. Inspect the walls and ceilings for moisture or previous moisture damage. If the apartment smells "damp" then ask the landlord to perform an environmental evaluation for mold. If they refuse you can get kits from home improvement stores.