In order to only show the My account button for Expert+ users you should follow these steps:
1. Edit file qa-theme/<your-theme>/qa-theme.php
2. Add or merge (if it already exists) this function in the file:
public function initialize() {
parent::initialize();
if (in_array(qa_request_part(0), array('user', 'messages', 'account', 'favorites')) &&
qa_get_logged_in_level() < QA_USER_LEVEL_EXPERT) {
unset($this->content['navigation']['sub']['account']);
}
}