Opening a window is a good idea while operating any gas appliance especially if you feel tightness in your chest, dizziness, headaches and irritability while operating an appliance. These are symptoms of carbon monoxide toxicity and can be deadly, so prudence and safety are the practice.
After discussing this with you on-the-air I suspect that the oxygen is less the issue and excessive moisture is likely to contribute to the tightness in your chest. This feeling of tightness is your body communicating possible respiratory distress.
I heard you say that high humidity is a persistent problem in this house all year round. I suggest that you address this internal humidity problem and maintain the relative humidity between 30% and 55% inside your home all the time. Insects and dust mites thrive in your house when relative humidity is above 50%. These insects and parasites can be detrimental to your health maintaining good indoor air quality.
Excessive moisture is Mother Nature’s primary tool in turning us all back into dust, so please control the humidity inside your house. Your gas fireplace can introduce large quantities of water vapor inside your house while it is burning. Water vapor is a large by-product of burning natural gas. So opening a window can help introduce oxygen and fresh air. I believe excessive moisture is a health threat in your home.