Should I Be Getting Overtime For This Or Drop It?

I work as a custodian for a university, it’s a state Job. If it matters I work full time and am a 21F living paycheck to paycheck on top of two small side Jobs so it’s rough out here. Not sure who to ask about this so I hope it’s the right place

For context the part-time employee that would do trash runs on the weekend left and they decided to have everyone in facilities take turns covering those weekends until they find a replacement. It’s been almost 3 months and they haven’t found anyone or they’re not looking. It was finally my turn and I had to work this previous weekend and soon the next.

The issue I have is that the bosses are adamantly against overtime unless it’s preauthorized for events. So instead of getting paid for an extra 4 hours they want us to cut 4 hours out of our work week to make up for it. Which sucks when you have less time to get your own building done and up to par for the week. On Friday I ended up working beyond the time I was supposed to leave by 20 minutes because the men’s room had serious issues, very gross and guys were in there so it took forever to get in. On top of that I couldn’t take my 30 minute lunch break unless I wanted to stay even longer. Maybe that’s on me but then they would have been mad I left it trashed. Then on Saturday my supervisor worked with me to show me the buildings I haven’t been in. She was on the phone and it made us stay an extra half hour.

Today when submitting my time sheet she told me I got the times wrong and I should have no more than the average hours and no less. So I asked about how to put in the extra time I worked. She said that’s on me and I should ask the bosses (one of whom Just doesn’t seem to like me for some reason.) This is the same supervisor that had us clock out and keep working for 20 minutes once so that the bosses wouldn’t get mad about overtime.

Should I drop it an Just not get paid for the extra work? I’m sorta a push over and don’t want to ruffle feathers but it’s frustrating