All of the rashes mentioned I can relate to. Some people, especially with fair and sensitive skin should not excessively sweat as they do not have enough sweat glands. Could very well be genetic for example, my ancestors were all from cold northern climates and didn’t need to sweat as much as those in warm southern climates. The month I started Bikram Yoga, I developed heat rashes in the crooks of my arms and legs. I went to my General Practitioner who said very confidently that it was eczema and gave me a topical steroid which temporarily helped but came back with continuation of Bikram Yoga. Long story short, the Bikram caused over sweating and stimulation of my sweat glands and caused many rashes related to heat all over my body.
I was checked by various doctors including 3 allergy specialists and 3 dermatologists. One could link my rashes back to Bikram and the excess sweating. Allergies contributed to the itching but was not the reason for the rash. The rash led to eczema and other fungal issues on my skin.
Those who mentioned they are suffering from something similar, Google “heat rash”, specifically Maliaria under a website called emedicinehealth.
Bikram just may not be for you as it wasn’t for me. Try a non heated yoga studio. Some studios even have Bikram postures in a non heated room. The Bikram sequence is great and well balanced but there are many health reasons why some people just aren’t meant to do it in intolerable and unnecessary heat and humidity.