Marek, I am not aware of effects like yours being reported from exposure to much stronger LF fields at LORAN sites and other transmitting facilities. The magnetic field 2 meters from a loading coil handling 500 watts might be near or slightly above accepted limits for human exposure at low frequencies, but not greatly in excess.
However, as you surmise, you are not just being exposed to LF alone.
The two middle items on your list are, far and away, the most likely sources. In addition to the normal high-frequency components of the switching waveform, it is possible for there to be surprising amounts of UHF energy from parasitic oscillations during the on/off transitions of the FETs. This depends a lot on circuit layout.
Your symptoms sound very much like a story I heard in my younger days of an amateur radio operator whose unshielded high-power HF rig was emitting parasitic oscillations in the high UHF range. He, too, experienced a rash and other allergy or flu-like symptoms, and eventually developed eye problems. I would very much encourage you shield the rig adequately before further operation!