Hydrocortisone thins the skin when used frequently, I recommend against applying it on or around the crotch area. Use diaper rash ointment (Zinc) until the skin is no longer inflamed. I recommend The Ritual Chamois Cream before a ride. And, Assos bib shorts, but not the thickest padded model.

In addition to my four previous recommendations, something else that worked for me was increasing stance width.

It is possible you have a fungal infection (Candidiasis or Tinea Cruris). For treatment I recommend Miconazole Nitrate Vaginal Cream (4%). If you can only locate prefilled vaginal applicators don't dismiss the product, it's even easier to apply topically using the plunger.