My skin can get pretty sensitive to heat, temperature change, stress, as well as the usual embarrassment factor. It's an extreme case of flushing in those kinds of situations. Anyway, is there something that I can buy (that is inexpensive) and use to cover up the blotchy redness? I get it on my face, neck, and upper arms. I am a fair skinned person, so I don't want to do any sort of tanning.

Yes, changes in the weather and other factors can make your face turn
Red, especially if your skin is fair. Red blood cells can also cause this. When you are hot, blood flow is sent to the skin and face. That is why you turn red when you are hot.

There's a make up line called "Bare Minerals" and it works great on red or blotchy skin. It's made from pure minerals and it has no additives. All you have to do is dip your brush in it and tap off the excess, then brush it on your face. It will cover the redness and even out your skin tone.