I get it too, meggymoo. As a child I used to burn, there was a short window between about 14 & 18 where actually tanned, and then I started with heat rash, which I've had preety much all the time ever since.
However when we lived in the US for 4 years - long hot summers, like lucy in Spain - I either didn't get it or it went away after a while. I think the problem here is that it's never sunny for long enough for your skin to get used to it so you get sun, flare-up, weather changes, rash dies down, sun comes out again, flare-up again etc.
Trying Potty's pre-rash anti-histamines sounds like your best bet but I would still use a high factor sunblock if you can't resist short sleeves and shorts.
I would love smooth brown skin but am resigned to never having it!