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I think people will figure something out when they begin to study the magical limb disappearing event and they find out you're the only person alive who was unaffected.
"I was born with an extra arm"
Pics or it didn't happen
Turns out it was the third leg
3rd wish: no one ever will figure out i was the reason for the limb disappearance
People will have to rationalize your existence somehow. Being unable to ignore that you're the one person left on the planet with 4 limbs, everyone you meet now immediately labels you a freak and you find yourself ousted from society.
Or they just blank every conversation you have with them from their memory. Meeting people would be like meeting them for the first time. That's some monkey paw.
The second wish could make forward by "however one in 1.3 million people don't randomly instantly lose a limb, instead they lose theirs randomly over time" that's enough of a cushion where you wouldn't be too weird.
I am sure the mystery of disappearing limbs will FAR overtake the one person who wasn't affected. Worldwide panic and who knows what else. You could also wish 99% of people lose a random limb, and that would mean 70 million people would still have all their limbs.
It might not be obvious, depending on what counts as a "limb". Plus maybe OP already is missing one?