need feedback on radiator heating systems and carbon monoxide
If your carbon monoxide detector is going off, you have a carbon monoxide problem. Contact your utility or local emergency services for a more thorough test. The symptoms you describe are consistent with early stages of carbon monoxide poisoning.

If your radiators heat with hot water or steam, or another system other than forced air, you will not have return ducts. That is normal. Carbon monoxide inside homes typically originates from a gas-burning appliance directly -- so in your case it would be gases coming up from a heater or boiler (probably in the basement). Alternatively, it could be that the exhaust duct / chimney is leaking into your apartment, rather than completely exhausting outdoors.

Get this looked at right away by professionals. BE VERY CAREFUL and do not venture downstairs; if the CO problem is bad in your apartment, it might be much worse in the immediate surroundings of the heater. Be safe!