Shady manager

Hello , I’m coming today because I have a certain dilemma. Last Thursday my manager verbally approved of me and a co-worker switching our off days ( mom-tues to weds-thurs) he approved of it & at the very last of my shift he told us to write it down on a random of sheet of paper he never provided. I asked him multiple if I had to put it on a 71 & he repeatedly told me no that I didn’t need to, another manager was aware & around to hear this confirmation . I wasn’t aware that his off days were Friday-Saturday & he didn’t return until Sunday when I approached him and asked him (he had an attitude a very nasty one) he told me that it was too but I’ve been asked before to switch my days without having to sign a sheet. I searched up the contract and fact proved it with chatgpt and it stated that I didn’t need to sign a piece of paper if it was agreed verbally upon beforehand. I have an appointment tomorrow I’m willing to work half the shift considering my appointment is at 3:30pm I start @11 but they claim that they’re short but in reality they don’t want to hold their regulars accountable. I recently got done having the flu & just returned I really dont want to call off but I feel like this isnt right nor fair