An easy test is to roll up a sheet of newpaper, light it, and hold it in the firebox -- with the flue open, of course. There may be a downdraft at first because cold air tends to flow downward. But then the heat from the lit newspaper should create an updraft. If that does not happen, you probably have some kind of clog in the chimney. It might have been cause by a chimney cleaning that was not done right.

If the problem started immediately after you had the chimney cleaned, it's possible that something the chimney sweep did, or didn't do, is the cause. Maybe you should have him look again or, if you're not sure of his competence and honesty, have someone else look at it.