Wheeze and Sigh

Wheeze

The word wheeze means to make a whistling sound due to difficult breathing. It implies illness or a disease such as asthma.
EX: If you can hear the baby wheeze, it is time to take her to Accident and Emergency. Asthma can manifest itself through difficult breathing.
EX: I wheeze whenever I have a chest cold. It makes me feel like I am gasping for air even though it is just an annoying sound.
The phrase good wheeze refers to an effective trick or idea. It is most common in British English. American people would tend to use gee whiz instead.
EX: You plan to pour the bucket of water over his head when he walks in? That's a stroke of genius! Gee whiz!
EX: We should listen to Billy's idea. He is infamous for having a good wheeze. We can come up with a different plan if we do not like his.

Sigh

The verb to sigh means to breathe out in a way that you can hear. It implies sorrow or weariness and can be used as a noun.
EX: My mother let out a sigh when she saw the mess she had to tidy up in the kitchen after Jan and I made brownies.
EX: Her sigh expressed her heartbreak. She did not want to come out and say that she wished her best friend had not moved away.
The popular phrase breathe a sigh of relief means to feel relief at the outcome of an event or situation.
EX: Once you get your letter of acceptance, you will breathe a sigh of relief. Until then, do not bother to waste a thought on it.
EX: My mother breathed a sigh of relief when we arrived home safely last night. She gets hot and bothered when we stay out past our curfew.