Is there a luggage storage facility at the mall?

It should have one, if it doesn't you could try dolphin mall which isn't to far from international mall.

Yes

Macy's has a department just for travel items

They should have luggage stores , but not all luggage store but that areas of just luggages yes.

This is a Google managed site. Refusal to check a website or make a phone call is very LAZY.

THEY HAVE LUGGAGE STORES BOTH IN MIAMI INTERNATIONAL AND IN DOLPHIN MALL, BUT NO LUGGAGE STORAGES