I am looking for a word that means similar to driving out (a fly), so you 've got a fly or a bird flown into your home and you want to chase it out. It sounds like swish or woosh something. Does Anyone have any idea?
You may be thinking of shoo, though it means to chase away as opposed to out, especially in the sense of scattering pests as opposed to birds or bats which may have accidentally flown inside:
interj. Used to frighten away animals or birds.
tr.v. To drive or frighten away by or as if by crying "shoo."
[AHD]. ODO calls it A natural exclamation: first recorded in late Middle English. The verb use dates from the early 17th century.
In American English (at least in the South), shoo-fly or shoofly is a term of its own; the Online Etymology Dictionary refers to it as an admonition to a pest.
Shoo, fly or shoo-fly are known from folk songs like Shoo, Fly, Don't Bother Me and Skip to My Lou, but have made their way into terms where the connection is unclear— a type of flask, a type of rocking horse, a type of pipeline or railroad, a type of punch. Most of these are associated with the South, though the most famous, shoofly pie, is closely associated with the Amish, who are concentrated in Pennsylvania and Ohio. One theory is that the molasses in the pie attracts flies, who must be shooed away; as it is a pie of molasses and crumbs, however, shoofly became associated with something temporary or makeshift.
You can swat a fly (this fits with your "swish" and "woosh" idea). It doesn't necessarily imply though that you're tying to chase the fly away--it can also imply that you're trying to kill the fly.