You are correct, you "have full permission to alter, distribute, and use it as long as it's for non-commercial purposes". You own the copyright on the image as you have created it, you are simply prohibited from using that image for commercial purposes, so you cannot sell it, or make it a part of another saleable product or work. But you can put it in an image gallery online, show it to friends, even have it printed for your wall or a t-shirt (as long as you don't sell the prints or the shirt), no problems there.
- Oshyan