You should be able to view all of you skins in the client.

"I think and i believe others do too, that you should be able to view your skins in the champions tab in your profile OR in a other one. This would be a good addition to the game and personally i have been wanting this for a long time, also you could see them in alphabetical, price , rarity categories."

I posted this in the PBE forums 7months ago (my acc is now locked) for being off. I googled my name and saw this and decided to post it on the live forums because maybe it would of been noticed here. I don't know if someone has suggested an idea like this and riot had rejected it.