To breathe in a gasping, strained way is to wheeze. You might not know you're allergic to cats until you walk into the house your friend shares with six felines and start to wheeze.
A particular raspy, whistling kind of breathing characterizes a wheeze. You might wheeze because you've got a bad cold, or because your asthma is acting up after that half marathon you just ran. It can be scary to wheeze sometimes, because it feels like you're not getting quite as much air as you need with each breath. Wheeze shares a Scandinavian root with the Old Norse hvoesa, "to hiss."