There's only one Head Boy and Girl every year, so it wouldn't really be "of your house", but either that or prefect- although maybe being a Head would be too much responsibility, so I'll go with Prefect

But being Head boy/girl means you were also a prefect.

Not necessarily. James was Head Boy and he wasn't ever a prefect

James was head boy? I thought it was Remus.

Nope, James was Head Boy along with Lily- Remus was just a prefect

Oh.

Yeah, I meant "house."