If you aren't losing coolant then the heater core isn't leaking.

You can test the pressure of the cooling system with the engine off. The monovalve should be full open with the engine off. If it's holding pressure, the heater core's not leaking... unless it only leaks when it's hot.

There is only one outside air intake in the area of the windshield wipers. Maybe you are sucking in fumes and when you switch to AC/cooling the system switches to recirculate which shuts out outside air.

If your car has a manual recirculate button, engage it when you're not getting headaches then switch to heat mode. You should get 5 minutes in heat mode before the recirc mode self-cancels.

You might try a carbon monoxide detector from Home Depot. It should be sensitive enough to work in your car. I understand that you're supposed to mount a CO detector low, unlike a smoke detector that you mount high. Maybe CO stays in the footwells when it's cold and rises to the level of your nose when it's warm.

FWIW, I get headaches in any environment that's too warm for my taste. That includes cars, buildings and towns.

Sixto
95 S420
87 300SDL
83 300SD