What is the way to get rid of a constant feeling that one is a source of bad luck for those around them, especially after the repeated failure of their close ones in their exams after interacting with them, and what is the ruling on others accusing them of that?

What this person is experiencing is a form of pessimism and evil omens, which are forbidden. A Muslim must beware of them by ignoring them and relying on Allah. When feeling something of this nature, one should say: "O Allah, there is no good except Your good, and no evil omen except Your omen, and there is no god besides You."