These days I've been cleaning my house for my coming baby.
There are lots of stuff that I won't use anymore, so I've tried to sell some of them, which are still intact, through an auction.
【！】"by the auction" is ok, but native speakers say "on an auction".
Also you used "The" but there are many different auctions, such as Ebay, or auctions you actually go to, but didn't specify a specific one.
It was just cards and I got it for free, so I had thought no one might buy them or if not, they would be sold for at most 1,000 yen.
Astonishingly, however, a woman bought them for 6,000yen. What a rich woman she is!
Being made by a big name brand, I will never buy them for such amount of money!
Actually, according the buyer, she'd been looking for them for a long time.
Anyhow, I was very happy.