how to call out for moving/good excuses to call out w/o coverage

I have to move on short notice tomorrow and I could not get the day off in advance - I asked two coworkers to cover for me, but neither ended up responding. I feel like if I call out with the excuse of being sick, its going to be an easily discoverable lie (especially bc I am also on the shitlist of another coworker for unrelated reasons, so one of them snitching is a concern lol.) along with that, my managers DO know I'm moving in the next few days (I havent had a set date until yesterday, but have been preparing for the move the last 6 mo), so it seems like a flimsy excuse.

we're pretty understaffed but not hiring, so I really only have two people to cover for me ever (2 people on shift at a time, 4 people hired for our position in total including me). I don't really feel like I'm in the position to call out on short notice, especially after having a recent shift covered for other moving related things - but I NEED to get the day off as it's an overnight position and I need to be available during that day before to move, and if I can help it I don't want to pull an all nighter plus a 3 hour bus ride after the end of my shift at 6am back to the new place. I don't really have anyone I feel like I can ask, I am embarrassingly old to be this anxious about a minimum wage job but I can't afford to lose it, Im a bit of a worrywart and I just do not know how I should go about this