Bluetooth is ludicrously low energy. There's no way it could have any effects whatsoever on your cells. Microwaves in the 2.4 and 5GHz wavelengths can't affect chemical reactions such as those occurring in our cells, the energy imparted is too low, and is mainly absorbed by the body's water content instead, which is harmless. You're far more affected by sitting in front of an open fireplace.
Why would the battery concern you? There's a teensy-tiny risk it might short and catch fire of course, like with pretty much any lithium galvanic cell, but that's so insignificant you might as well worry your fridge will fall over you and maim you the next time you open the fridge door... So TL: DR: batteries are not a source of EM radiation.
Airtravel, unlike cellular, wifi and BT radios, actually DOES expose you to actual, real "radiation" (meaning ionizing radiation, coming from the sun and deep space cosmic rays and whatnot), but it is certainly not "brutal" in any meaning of the word. It's a slight elevation of exposure compared to what you'll receive - on average - right here on the ground; air crews often work for decades flying on aircraft with little in the way of ill effects to show for it. Yeah, flying a lot is an increased risk factor for cancer, but it doesn't mean you will actually GET cancer, or that it will be a form of cancer caused by ionizing rays.
It could instead be something genetic, or caused by say, your diet, smoking and so on.
If you live in areas with certain kinds of bedrock (granite for example can have a slight uranium content) or in a home built out of certain kinds of concrete that emits radon, you could receive more than what you'd get from air travel.
EM sensitivity is psychosomatic, and does not actually exist in real life. There's no scientific evidence that it does exist, and no proper double-blind study ever made has been able to establish any links that it does exist.
I think maybe the reason people (perhaps like you, I don't really know) react to cell phones and computers and whatnot is because they don't really understand how these devices work, or even how basic, fundamental tenets of our universe itself works. If you don't know how a thing functions, it might seem suspicious or mildly frightening to you. One might therefore mistakenly come to associate something like wifi or cellphones with headaches, or general feelings of unwellness or whatever, and the body would react correspondingly to produce those symptoms if you know you're in the presence of that which worries you.
This, unlike EM sensitivity, is well established in many medical studies.
