What should I do, I won a giveaway then accidentally gave it away

you get reported thats what

how did you mix that up

If you're that worried about being reported, maybe you can buy the game you won?

Won games have to be activated by you. You could either get yourself a copy and activate that, or take a suspension or whatever the punishment is.

Talk to support. I can understand how the C&P accident can happen, because I have done similar. Not with giveaways, luckily, but when C&P lots of stuff, and you thought you hit C then go to paste and it was the previous thing you C, not the new thing. Usually happens when my fingers are moving too fast while typing and I don't hit the C completely so it doesn't register the Copy command since the key didn't get pressed all the way. All you can do is show them the screen caps of the accidental email, and TALK to them, and see from there. Accidents happen, and if you are at work, doing stuff on steam/internet when you aren't supposed to, there is that added pressure that can make you easily slip up.

you should invite me to your steam group xD

If it's a humble bundle link, you (or perhaps the original buyer of the game, so the person who gave it to you) could contact support and ask them to remove it from the account. Then you activate it on yours.
Is that allowed?

Hmm, damn, that sucks for you. You can try that:

Try contacting Steamgifts support to find a solution to get you out of this mess.
Buy the game again to activate to your own account.

I don't think Steamgifts actually cares providing no one complains, so if you eat the loss and the other guy is happy accidentally getting the other game and willing to mark it as gift received then that should be the end of that. Alternatively you'd be looking at a not received mark against you despite the other game he got.

Since Steamgifts doesn't actually take temporary possession of any gifts they can't really police it beyond fielding complaints and the negative gift not receved/sent marks against your account.

First, did you try talking to the person who activated the wrong game to have it sorted out? And based on your last comment, that person got both RIGHT and WRONG game?

EDIT: Removed second question.

Since you marked it as received, I take it it's the most recent win on your profile?

You could easily earn coins over on TremorGames.com for it. I just looked up its "cost" there. You'd likely be able to get it within a few hours/a day depending on your region.

If you have a win, that isn't found on your profile, it doesn't matter why, it is something that can get you suspended.

Obviously, it isn't the fault of the original gifter, so it would be rude to let them have a black mark on their profile, but unless you want to get the game elsewhere, you will need to deal with a suspension the next time someone mentions the lack to support, along with possible backlists.

If it is a game that has been bundled, it should be easy enough to get through trading.

What game was it?