@DRS_Design Expansion packs are a different matter entirely. You'll need to contact EA customer support and ask about the status of the EP, not just whether it's on your account but whether the product code is active and valid. An invalid code is the usual reason an EP or SP will install but not show up in the lanucher.
Codes can be blocked or invalidated for multiple reasons, including when the content is originally stolen from EA; it doesn't matter how many hands it's been through since then or that the end user had no idea the code wasn't legitimate. Another possible cause is a bad account merge, and there are others. But in any case, only support can address this issue, whether that means removing a bad code alone or removing it and adding back the DLC.
I would strongly recommend using live chat rather than email. If you don't see the option, try this link:
Make sure you're signed into an EA site (this one is fine) before clicking the link and that the location in the lower-right corner of the browser window is set to U.S. or U.K.
