I don't want new clothing. I want a different avatar. I'm a guy. This avatar is a girl. I don't want a female avatar. Do I have to register all over again just to change avatars?
No, you don't need to register to change your avatar's gender. An avatar is strictly speaking genderless. What ever you dress it with or tack on will make you appear as a gender (or even as something genderless, if you want.) It's one of the many, many customization options you have in SL for your avatar.
Your current avatar has a female appearance. In your inventory you'll have items which can give your avatar a male appearance, such as a shape, hair and clothes. You can also find/buy such items in Second Life itself or learn how to make them yourself.