Can My Boss Tell Us We Can’t Wear Gloves At Work Anymore?

i work behind the bar at a restaurant in los angeles. my hands were getting extremely dry and got to the point where they would bleed because of how often i had to wash them, so i got some lotion and started wearing gloves more often. i change them very frequently & so do my coworkers, we’re all aware that we have to change them as often as we’d wash our hands. we got audited recently & today we get a message from our GM saying from now on we can only wear gloves when prepping fruit. i figured my best option now is to get a doctors note about my dry hands. can he do this though?