Unisex Restrooms at Work & Periods

My work recently moved into a new building and all restrooms are unisex and I am unfortunately the only female working in the building. I am thinking of asking my manager if one of the restrooms can be women’s only because I feel awkward when I have my period and I have to share the bathroom with a ton of dudes and we don’t have the container for pads/feminine products. We also are cleaning the bathrooms ourselves so whoever is cleaning it the days I’m bleeding would know I’m on my period... I know that everyone is an adult and knows periods happen but I think it’s different when it’s your coworker vs your wife/daughters

Can I have some advice on how I should bring it up to my manager? TIA 😖

Note: We have 4 bathrooms and 12 employees