Is there a single word in English to describe someone who is too worried about their health and even thinks they are sick, thus, taking frequent clinical tests or taking too much predictive medication,etc.
The word is hypochondriac and they suffer from hypochondria.
A person who is abnormally anxious about their health.
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..
You call them a hypochondriac. A similar term is valetudinarian:
A person who is unduly anxious about their health.
It usually refers to people who really are frail but fuss about it so obsessively that they avoid actually getting sick. The Free Dictionary puts it better:
A sickly or weak person, especially one who is constantly and morbidly concerned with his or her health.
If you wanted to give a hypochondriac the benefit of the doubt, or just humour them, this would be a less pejorative word. See World Wide Words for a good description with examples. In Jane Austen's novel Emma, the heroine's father Mr Woodhouse is a classic valetudinarian.
The word is from Latin valetudinarius = in ill health.