Is your damper wide open when you burn wood?

Yes. We also have been making them toward the back to help.

Well, your draw isn't strong enough to keep all the smoke going up the flue. Cracking a window might improve it. You're not using a ceiling fan near the fireplace are you? Your chimney top should be above the highest point of your roof. Is it? Do you have a tile or metal flue pipe? You can add an extension to get the extra height. Lots of variables.

If all else fails, get an insert.

Adding Glass Doors to the fireplace that are capable of being burned with the doors closed can help prevent this. Most glass doors must be open when burning. I can help you get the ones that can be burned with the doors closed. They will need to be custom made to fit.

Follow the instructions here to get help: Fireplace Treatments