I read the word sometime ago and can't remember it. the smell of the perfume of someone after he/she walks by..
The word is unsurprisingly from French: sillage.
Sillage (pronounced as see-yazh) is a term used to describe a scented trail left by the fragrance wearer. It comes from the French word for “wake,” as in the trail left in the sky by an airplane or on the water by a boat. Sillage defines how fragrance diffuses around the wearer, and a strong sillage means that a fragrance projects well.
Though, sillage technically defines the degree of the scent of a perfume left behind also and it is a term used in perfumery jargon1. There are different levels of sillage and there is even the term monster sillage to define the strongest fragrance trail. This Elle article talks about sillage in detail.
1 [oxforddictionaries] sillage - the degree to which a perfume’s fragrance lingers in the air when worn
Additionally, wake, slipstream or trail (of a perfume) is used also and they are more suitable for everyday or novelistic speech.
He started to mumble a phony apology when the wake of her perfume struck him like a strong whiskey.
[The Stewards: A Fight to the Death of Animal Survival by Robert Sherretta (2010)]
She returned the crystal bottle with the rubber squeeze ball and its silken tassel to her dresser, and grabbing her nutria jacket, she breezed out of the apartment,leaving us in the trail of her perfume.
[Good-bye to the Mermaids: A Childhood Lost in Hitler's Berlin by Karin Finell - 2006]
I followed behind her in the slipstream of her perfume, past a polished wooden staircase and into a long, wainscoted hallway.
[The Last Heir: A Mystery by Chuck Greaves (2014)]
You may want the word waft as it carries the sense of the movement of air carrying the smell along:
It can be used as a verb:
Pass or cause to pass easily or gently through or as if through the air.
The smell of perfume wafted out of the department store.
or as a noun:
A gentle movement of air.
I detected a waft of cheap perfume.
The word scent could fit here, as it can be used to describe a (often pleasant) smell which fills the air as the result of someone or something.
For example, "as the woman passed by, we caught the scent of her perfume".
If you wish to connote that the smell is unpleasant, you could consider miasma, which the American Heritage Dictionary defines as:
A noxious atmosphere or influence.
a. A poisonous atmosphere formerly thought to rise from swamps and putrid matter and cause disease.
b. A thick vaporous atmosphere or emanation
(Puns on "my asthma" are left as an exercise to the reader.)