Hello,
From the symptoms that you have described,they can be folliculitis or lichen nitidus.Lichen nitidus characterized by 1-2 mm, discrete and uniform, shiny, flat-topped, pale flesh-colored or reddish-brown papules.
Generally, lichen nitidus is asymptomatic and self-limited; therefore, no treatment is required.However in severe cases,topical glucocorticocoids can be prescribed.
I hope that helps. Take care and pls do keep me posted on how you are doing or in case you have additional queries. Kind regards.
My father has similar white bumps on his arms and hands, when Ive asked him about them hes said they are simply caused by ageing and the fact you say they may be heat rashes links in as well since he lives in Dubai and didnt have them before hand. Dont know if that will help at all, hope it stops you worrying as much!