Okay, go send a support ticket explaining the situation. If you can, provide as much info as you can in your said ticket to prove you own that said account and it'll help them find it. Things such as recent purchase, rp or ip, division, Obviously both account and summoner name, etc. They'll find it for you and bring it back into your hands.
From the sounds of it, someone had gained access to your account while you were offline and made the purchase to keep it away from you. Most likely the password is different, and the name might have gotten a change too (But they can check for recent name changes too.) While you wait, I highly recommend doing scans on your computer in the chance of a keylog or trojan stealing your stuff. Trust me, if the account vanishing away was bad, imagine if they got your credit card too. Check your bank if you think they did any purchases on it and such.