For the nappy rash giving it "air time" was the one thing that worked best for my LO. Do make sure you are drying their genitals very well before applying any creams too. We did use Sudocrem and Metanium, and the Metanium was working better than Sudocrem, but I'm not sure if either is available in the US (we are in the UK). As for the heat rash, I don't have any experience with it, but we did end up using a steroid cream for the nappy rash because it was really bad and it helped a lot, so I reckon you should be fine to use it. The recommendation though was not to use it for more than 5 days and to use it only once a day because baby's skin is quite delicate, so if you end up using it make sure to follow medical advice on how long to use it for. And of course the usual things would be to make sure baby is in loose clothing, that is well hydrated (if breastfeeding you can offer some extra feeds throughout the day) and avoid using any bubbles, soaps or gels when bathing (just top n tail kinda thing).
Swap to using cotton pads and water for wiping little ones area and I swear by sudocreme for all types of rashes/dermatitis