There a number of things that can cause a draft problem with a fireplace. Given the super cold temperatures this winter, make sure you are taking time to warm chimney before building a big fire. Sometimes chimneys that are very cold force smoke to fall rather than allowing it to drift up. As the smoke and gases rise, the cold chimney cools the air enough that it falls instead of rising. Build a small fire before a roaring one.
It's also a good idea to check how much comnustion air you have. Fires use quite a bit and if your home is well insulated you may not have enough. Opening a window helps. Newer fireplaces have built in combustion air systems that pull air directly from outside.
Next, inspect the chimney for blockages - you should look for things like debris, animal nests, etc. The best way to do this is on the roof looking down. If you have to hire someone, I would recommend a home inspector who has no stake in making money off of what he or she may find. If you hire a chimney company to inspect, make sure they are reputable, certified and can show you proof of what they find with video and/or pictures. Chimhey height can also impact the draft. Chimneys are supposed to follow the 2/10 rule. If you measure down two feet from the chimney, no part of the building should be within a 10 foot radius.
If you've checked all of that and still cannot get to the bottom of your problem, you may need find a good chimney contractor to further investigate the problem. Good luck!