I live in a 2 bed house with with a with an open fire in front room dining room and main bedroom. Today for the first time I lite a fire in?

Was swept Friday. It's a straight up chimney no dampers. Fire in the bedroom above is fine no smell. It's just the one in the next room. Strong draught coming back down and still smells sooty if makes sense. Fires been lite 4 hours

A few people here understand how a fireplace works, but most don't.

There are doors (dampers) above the fireplace that must be OPENED every time you light a fire (so the smoke can go up the chimney and out of the house) and CLOSED every time the fire is finished.

Shine a light up inside the fireplace and see the levers/chains/whatever.

If you do not plan to use the fireplace in the dining room, one thing you can do is get a piece of fiberglass insulation bat and push it up in the dining room fireplace outlet. That will act like a damper and keep the smoke from coming down in the room.

Burning wood or coal is dangerous to your health and that of your neighbors. Do everyone a favor and heat your dwelling with natural gas. Using a fireplace is self defeating because cold air has to rush in from outside to replace what has gone up the chimney. If not, your house would be in a vacuum and there would be no fresh air to breathe and you would soon suffocate. Google "the dangers of wood smoke".

Might just be weather conditions. If you had chimneys swept and it persists, you need advice from a chimney sweep or a builder. You can get cowls fitted to the top of the chimneys to eliminate down drafts.

yeah it is good

Yeah dampness or because it hasn't been used in awhile. I'd run the fire for awhile to see if that dissipates and if not then it might be something else to look into.

All chiminies should be checked by a chimney sweep yearly. The are the pros on this.

Get the chimneys swept.

did you open the damper?