There are two ways you can change the appearance of your character, one which is 'official', and one which is a console hack.
If you have the Dawnguard expansion, you can go to see Galathil in The Ragged Flagon in Rifton, who will allow you to change your character's appearance for 1000 gold.
If you don't want to do this, and are OK with messing about in the console [PC only] then drop to console and then type showracemenu - you'll be able to make any changes you want. Just don't go mad with the changes [i.e. don't change race], since you can mess things up here. It's better, I feel, and safer, to go the 'official' route and consult Galathil.