I generally get the characters to repeat the words and use a few ellipses. As long as it's in context, readers should understand. For example: James saw Anna sprinting round the corner towards him, her cheeks puffed and red. "It's Tony," she said at last when she was near. "He's...he's here. And another thing. He's asked to...asked to see you." Hopefully what I've said makes sense.
Don't put the wheezing in the dialogue. Put it in the narrative surrounding the dialogue. A pause is indicated by ellipses, but don't overdo it. Understated is better.
The others gave great answers, which, obviously answered your question. I would like to add a little footnote, though: If, for whatever reason, you wanted to insert the *sound* of wheezing, I would recommend something like: I heard Brown pounding up the stairs, followed by a thumping, fumbling sound indicating he'd tripped over the last few steps. Then I heard the steady clicking of Jane's heels on the hardwood floors. I pressed my ear against the door, straining to hear my captor's conversation. "Well? What did you find out?" That was Jane. /"Heehhh....heeehhh...."/ (Writing on my phone, no italics) "Why are you making that appalling noise?" "I just.../heehhh/...ran...all the way...up he-here from...the town..." There was a pause, filled only with sounds of Brown's ragged wheezing. Then, Jane asked, "And? Do you want a medal?"
Sometimes it's best not to underestimate your readers. I don't need dialogue hitting me over the head with what the writer should have told/shown me already.
You can either go: "The... the monster is... coming to... eat you up," Jane said. or(my preference): "The monster is coming to eat you up," Jane said, and paused for a moment to rest her hands on her knees and cough up phlegm.
Making your dialogue seem natural is great, but don't overdo it by throwing in lots of interruptions. Readers will stop caring. I would just give you character a pause outside of dialogue and indicate that they're having greater difficulty breathing.
That's pretty good, actually. I'd say do what works for your story. You can use ellipses or long dashes in dialogue, or reproduce the noise like ManOrAstroMan has done, or describe the sound, or just mention the person is wheezing. Any of these would work, in the right place.