If I need a license
As correctly pointed out by others. You technically don't need a license, but it's a good idea to have one.
In layman terms: since anybody who creates something automatically owns the intellectual property of his/her work, you are free to decide which rights you want to retain to yourself and which you are available to give to others. The two extremes here are "all rights reserved" and "public domain".
If you don't specify through a license what rights you grant to others and what rights you don't, the situation will be very confusing, as different countries default to different sets of rights.
my game to be totally free
Free as in "free beer" or free as in "freedom"? This normally translate in a "non commercial" license (free beer) or "FSF approved license" (freedom).
my game to be embedded on other websites
This is a relatively new problem related to the emerging of SaaS, or in other words to the fact you can let people use your software without them ever getting in touch with the software installation directly (so, without distributing it). You might be interested to tool into the Affero General Public Licence
no one else can re-distribute my game, unless it is under my name and not theirs
Also, if I need a license, where do I include it?
This is what the GNU says about license inclusion for the GPL. I would recommend to follow the same advice regardless of the license you will choose to use. The problem with enforcing licenses is never with the interpretation of the IP owner will... it's always on minor details of its implementation, which leave space for loopholes to be exploited by... well you know... THEM! ;)
Licenses that resonate in my mind reading at your requirements: GPL, AGPL, Creative Commons Attribution-NonCommercial