Looks like ozone rash to me. I've been that bad before. Worse probably. Did it ooze too? I've soaked my bed at night from it. Just slow down. Do it for only a few seconds 10-30 each week or maybe every two weeks. You've reached the point where you need to slow down. The reason it's worse on the more private areas is because that's where you sweat and/or rub. Just wait a couple of weeks and only do it for a few seconds and see how it is.
Another thing you can do if you're worried about the tent is get in the tub full of hot water and put the tube under you and let it bubble around you.
But even if you have the best sauna out there, you're going to get the rash. That means it's working, so it's good. If there's no rash, your not doing it long enough. You'll have months of the rash, so get used to it. You control how bad the rash is by the amonut of time you do it each time and how often.