Could u put a small bandaid over it? Or maybe one of those circular stickers people put over their acne marks, I’m pretty sure they have that at Walmart

Just make sure you clean them after your shift and really well. I think one of my holes got infected because it was 3 weeks to a month after I got my second holes and thought I could get away with not cleaning them well enough.
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Lazy hack: fold a clean tissue and place it between your ear and the headset

are you getting your lobes done, or something like cartilage? If it's just lobes, you'll be fine; you can keep the earpiece slightly above your lobes. It might feel a bit funny but it will prevent the earpiece from pressing up against a fresh piercing.

You may be able to do that for cartilage piercings too, just keep it lower instead of higher. If it's a conch or tragus or something though lol you might just have to be very very gentle