You're getting a negative draft. It could be that the height of the chimney is too short, there are trees nearby, or the distance from the roof pitch is too short requiring the height of the chimney to be raised.
What happens when you open a window a bit and light the FP?

Thank you for your response, Christopherh. I don't think we've tried opening a window. I'll ask my husband to do that. I'm a bit nervous to light it again because the last time we tried, the smoke smell took several days to leave. Ew.

Here's a link to a pretty good article that may solve your problem. Hope it helps.

Here is a link that might be useful: ARTICLES - Wood - How to Start a Wood Fire

What type of chimney is it, how many stories, is there an ash dump(hole in fireplace floor where ashes go)? The chimney needs to be able to warm up as that is really the engine that makes your fireplace work. I suspect it's not getting warm enough for some reason.