Inflammation (due to low output of anti-inflammatory steroids made in adrenals, delayed onset food allergies ) are possible.
Flu-like symptoms without an infection are possible.
Increased susceptibility to infections are possible.
To be honest, I have no idea what's going on in this case.
I have just leaned that many of the symptoms are interconnected ( diet & sleep, tyroid and adrenals, allergies & inflammation) and if you follow the general: DIET, YOGA, VITAMINS... path and eliminate stress as much as possible, the one part of the complex complication gets untangled and then the other can spontaneously resolve.