Is it okay to burn use my fireplace with a newborn in the house?

I live in a small apartment with a fireplace. Me and my husband love using the fireplace. It keeps it warmer in here than using our heater! We just had a baby, she is 13 days old today and I was wondering if I can still use it with her in the house. The fireplace doesn't have a gl thing on the front, just like this wire material. I don't know why. It seems unsafe to me. We open the flue on it and all the smoke goes out, but when we first light it, it smells really smokey in the house. I don't ever see any smoke, it's just the smell. Is it okay for us to use the fireplace with our newborn in the house?