Term for people who feel they have some disorder when they read about it
Solution 1:
I can think of hypochondriasis, although the term is not limited to reading about a disease nor is limited to psychological disorders (but any general illness). The word for a person who suffers from hypochondriasis is hypochondriac.
Somatization may also apply in certain cases.
Solution 2:
Wikipedia defines Medical student's disease as a specific form of hypochondriasis triggered by studying different diseases.