Plot hole: SPOILER: When Amy comes back, doctors would have checked her non-existent head wound from the "abduction", from where she supposedly lost that much blood. That would and should have revealed all of Amy's lies.
Plot hole: Amy calls the Police about the shed before going to Desi. They watch Nick's TV statement together. The shed is only searched by the police after the statement. Which would imply the police sat on the report for several days before investigating.
Answer: To my knowledge, the purpose of hitting herself was two-fold. First of all, a facial injury would support the idea that she was abused or in some sort of bad situation. And secondly, to help mildly alter her appearance, so she could blend in more. (Especially considering people were looking for her).
TedStixon