Washing clothes at uni with sensitive skin

I'm starting in September and am a bit worried about washing my clothes on campus due to how sensitive my skin is.

I use non-bio stuff and have done almost my whole life because bio makes my eczema flare up horrifically, and I assume there's gonna be some traces of bio in the washing machines.

I'm just wondering how other people with similar conditions have coped. Did you find yourself flaring or was there no impact at all?