Gym clothes

Okay, before you say that there are plenty of posts here discussing this topic, let me say this one has a catch! I am EXTREMELY allergic to 99% of laundry detergents. If it's not fragrance-free I will for sure have a rash that will last for days. That being said, I am having issues getting rid of sweat smell on some of my gym t-shirts and specially bras. My sleeveless shirts are fine, which makes me think it's probably armpit smell that's the issue here. Washing with my detergent only is not fixing it. I've also tried running a cycle with vinegar and then one with detergent, didn't seem to make a difference. Any suggestion that I could try? Please be aware that I really cannot even risk to use any harsh chemicals or anything scented. Thank youuuu!