This is an interesting topic. I've worked in aviation, and now use commercial carriers with some regularity. Fortunately, I have never experienced any of the symptoms you've described, aside from the occassional cold most likey brought on by close proximity.
I'd like to express a concern which I hope will not be taken as criticism, but as observation based on experience by someone who works daily with moderately complex statistical modeling.
Let's for a moment think about one of the symptoms raised in this thread, skin irritation. Were I to develop such a symptom during or shortly after a flight, it might be tempting to attribute the development to the flight.
This is called recency bias in statistics.
It is however possible that I had come in contact with something which caused said irritation either before the flight, and it took some time to be expressed, or after the flight, and the symptom was expressed quickly.
Self-diagnosis is a slippery slope, especially when one uses such terms as "chronic fatigue," which I think is a specific syndrome with documented diagnostic guidelines. Not being a physician, I doubt if I could accurately self-diagnose chronic fatigue syndrome in myself no matter how much medical literature I read.
What I am getting at here is that belief that something has occured does not necessarily mean that it has occured. Seemingly related events for which correlations have yet to be measured cannot automatically be assumed to be related.
Taking this one step futher, proof of causality requires that a clear signal be sent from A -> B. In the shorthand of formal logic:
If A, then B.
Not A, therefore, not B.
All that being said, I believe, based on casual observation and from the many things reliable people have told me about their own experience, that there is in fact a real health issue worthy of serious professional investigation.
I haven't spent any time researching the issue personally, but have no doubt epidemiologists are looking into it as we speak, as it's a field rich with the possibility for meaningful discovery.