Sauron had not made them. They were made by Celebrimbor, using knowledge he had learned from Sauron. They were kept secret from Sauron, and used to sustain the havens of the elves.

They didn't want to give them up because they knew once they did Rivendell and Lothlorien would fall. Plus Gandalf had the third one anyway.

I suppose at the beginning it mentions that there were three rings made for the elves, but does it really say that Sauron created them?

Celebrimbor made the three elven rings in secret. Sauron made the One Ring in secret. When it became known, it was too late for the Nine and the Seven, who had been made by Sauron himself, and thus the One Ring could control them. But for the Three, he had to acquire them to control them. Once he had (if he ever did) all their works would have been revealed and unmade in that moment.

That's why it was so important that they never fall into Sauron's hands, he had the ability and capacity to completely control them. So that's why they were only ever given to the greatest of the elven lords, or of course to Gandalf, one of the Maiar.

I'll pay attention this time around, now that you've brought it up!