My skin sometimes gets flushed when working out...and I may have a type of heat rash after on certain days...but not always and not often. It's almost like rosacia but not so severe. I also have very very dry eyes all the time. My Dr is doing tests for CTD (connective tissue disorders).
On the other hand, I can tan very easily and don't burn much. If your eyes are effected and you get skin problems that are intermittent, I would check for CTD's as well..it's an obvious one with those symptoms, although, with the flushing on contact - I'm not so sure about that one.
It does also sound like histamine, estrogen, or blood pressure issues.