Here is an odd situation, I believe. I THINK I created a Bitcoin account many years ago. It seems there was a site that gave bitcoin to people who signed up. It was just a few. My sister sent me a link. Problem is, I do not remember where it was. What information do I need to have to try and track down this account? Is it even possible?
Here are a couple of sites you might have used; Bitcoin Faucet at freebitcoins.appspot.com/getsome; Daily Bitcoins at dailybitcoins.org. Neither site is reachable.
I'm here to provide some more information to put your mind at ease. You most likely used a faucet to receive free bitcoin, and to do this you would need a public address. This would have been copied and pasted into the faucet's website. Now even if you still have this computer, not only would you have to have the public address, but also the private key to access the funds.
But in the past, 90% of the population had their private key stored on an exchange called Mt. Gox ... and this exchange went bankrupt 4 or so years ago.