What do you call someone who obsessively thinks they are sick? [closed]
The word is hypochondriac and they suffer from hypochondria.
noun
A person who is abnormally anxious about their health.[ODO]
ODO also gives the explanation of using hypo- ("under") rather than hyper- ("over") which one might expect if someone is overly anxious about something:
late Middle English: via late Latin from Greek hupokhondria, denoting the soft body area below the ribs, from hupo 'under' + khondros 'sternal cartilage'. Melancholy was originally thought to arise from the liver, gall bladder, spleen, etc..
Hypochondriac would seem to fit the bill.