I have the same problem.

I don't have Hearthfire in the View Downloadable Content window, but I do have the Valve TestApp thing Lord mentioned.
EDIT: Alright, I have it showing up now. To fix it, I did what Lannister did, minus the reinstalling. All you have to do is go to Properties (by right clicking Skyrim in the Library List) &--#62; Local Files. Then click on Verify Integrity of Game Cache. Then, once that finishes, click Defragment Cache Files. No reinstall required!

EDIT2: Hearthfire still appears as TestApp however, and I don't have the achievements. Further investigation will commence.
EDIT3: Alright, my method works. Despite the achievements not appearing, I'm still able to complete them.