I'm NT, so maybe I can't help much as far as relating, but have you tried different types of fabric? Cotton, satin, etc.? I doubt it will completely solve the problem, but it might help a little.
Or, if you don't wear skirts, you might be able to simply not wear underwear (when you aren't on your period). I knew a girl who did that. As long as you're wear pants or shorts, no one should be able to tell. But vaginal discharge might be a problem, I suppose.
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My name is Valerie. I am neurotypical. I have a sister (11) with Asperger's and a brother (20) who has been described as both "severely autistic" and "mentally retarded."