Can a faulty Catalytic Converter give me carbon monoxide poisoning?

I have had a severe headache and dizziness for over a week, I went to the ER and they said it was a sinus infection, yet I have no conjestion etc. My headache is also not around my eyes but rather the top of my top and temples......I have been taking antibiotics (for a sinus infection which I don't think I have) and have no improvement. I have a 2 hour commute to work and have been told I need to replace my cataltic converter, but have been putting it off because it's so expensive...but now I'm wondering if that is what is making me sick.