A person concerned about people staring at him is possibly experiencing a form of the "spotlight effect." According to the U.S. National Library of Medicine, the spotlight effect is the tendency for one to overestimate his own assumptions when it comes to evaluating how they are perceived by other people.
Psychology Today gives an example of the spotlight effect in which the author of an article writes about his experience walking through a crowded DMV with a small stain on his t-shirt. He notes his inability to estimate how many people were actually likely to have noticed it, given the fact that he is much more aware of the stain due to it being on his own shirt. The spotlight effect is ultimately a result of egocentrism, or in other words, the fact that each person is the center of their own experience.