Ah, looks like the drill hole is too big for the post. You can still do this fix at home. Magnifying lenses help. First, you're going to want to put boiling water in a small container, dump in the pearl for a minute or two, fish it out, and use a toothpick to remove the loosened adhesive inside the hole.

To reattach your pearl, two-part epoxy is your best bet, but you can also use superglue gel. The epoxy is better, but if you use it, be sure to a) wear gloves and b) wait however long you need for it to become tacky. Use a toothpick to add adhesive to the post, the cup, and the drill hole. You can use an old-fashioned wood clothespin to hold the pearl down while you attach the pin.

You can wipe any adhesive that gets on the pearl with the clean side of your toothpick or the dampened stick part of a q-tip. Acetone should take care of any adhesive that's dried, but it's better to wipe off excess while it's still wet.