There's an ongoing debate - that can actually become quite emotional and vocal - that tried to determine whether or not a relative should throw the baby shower. Traditionally, the view has been that a relative should not throw a baby shower, because it can appear that the relative is requesting gifts. Yet traditions change, and there are times when a sibling, or a cousin, or an aunt might be the ideal and somewhat convenient choice. So what should you do? To answer this, we can respond with the best, and sometimes most unsatisfying answer of them all: it depends. Sorry, but it really does depend. If you hail from a rather traditional or conventional background, it may be wise to see that a non-relative is in charge of the baby shower.
In addition, even if you, personally, are comfortable with a relative throwing the baby shower, some of your guests - who may be less comfortable with it than you - may object (or just whisper about it behind your back).
