This lists some differential diagnoses for intertrigo - conditions that are similar that should be ruled out or considered when diagnosing intertrigo:
"The differential diagnosis (other conditions that resemble intertrigo) include familial pemphigus, hidradenitis suppurativa, inverse psoriasis, staphylococcal or streptococcal impetigo, and seborrheic dermatitis. Group A strep can cause a rare form of streptococcal skin infection that produces a severe form of intertrigo affecting the neck creases, groin, perianal tissue, and toe webs of infants."
Have you had any actual testing on the area? Any cultures or biopsies?
Since you're getting an initial response to the cream, I'd say it at least started as fungal. Since the fluticasone cream didn't do anything, you should ask to get it swabbed and/or biopsied before they continue to just throw treatments at it that don't work.