I've not experienced the itching that you describe..
Generally if I get overheated -- which can occur on a hot and humid day if I'm out in the heat for more than an hour or so, and more quickly if I exert myself at all --
I first get very lightheaded and dizzy. I find it difficult to breathe. I weaken, then get very red in the face and upper torso (I'm light skinned so this is very noticeable.) I start to get anxious, then disoriented. I'll develop a fever.
Only getting inside under cool air (or packing my neck and wrists with ice packs to cool down) will relieve this.
I don't perspire -- perspiration is the body's normal way to cool: you sweat, the water comes to the surface of your skin, and the evaporation is what cools you. The lack of perspiration (which stopped when I developed MS) is the main problem, and of course when the weather is hot and humid the air is already damp, and so any perspiration that does exist doesn't evaporate -- causing my body core temperature to rise (the overheating), and then the symptoms begin.
When you see your doctor be sure to tell him about the problem you have with heat, too, and the rash -- there may be some connection there, and every bit of evidence is crucial to record until you get a diagnosis and know which are really important and which aren't.
...I am not a doctor, nor health professional, and don't pretend to be one, here.....