depends - if it was a key that you have inserted inside the giveaway, then yes, it should automatically be sent to me for use. In "Giveaways won" I would see a key. Instead, unfortunately, I just get a " --- ", meaning you may have not inserted the key.

If it was in form of a gift, I believe you still have to send it using steam - just putting "send" button indicates to the website that you did send the gift since, since steamgifts can't check if you did send the gift or not.

If its anything else (link to a website to redeem the gift) you can also put it as a key and it would show once you pressed "send".

Either way, if you believe you have done all the steps correctly, try contacting the steamgifts choosing the "support" section. I wouldn't want to mark you with "not recieved" for your first giveaway - that would pointlessly create a bad reputation for you and you don't need that.

Take your time, I'm in no hurry ;p