Yes, the pool store should sell small sheets of vinyl repair, along with a little can of the adhesive that goes with it. You can apply it yourself without draining the water.
Edit to add: When we had a large hole, the first patch got sucked right into it because it wasn't cut much bigger than the hole, plus the water was gushing out at such high pressure it took the patch right out. So keep that in mind when cutting your patch size.
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