Is the fear of a dreaded occurrence coming true, accompanied by an attempt to convince oneself that it will not happen, considered a bad omen or claiming knowledge of the unseen? And does this fear reach a degree for which a person is held accountable for a sin?

Perhaps what you are experiencing is pessimism and satanic whisperings. You should abandon this way of thinking and guard your tongue from what does not benefit you. Be optimistic and think well of Allah. Islam forbade and invalidated pessimism. What a person thinks or expects, be it good or bad, does not necessarily come to pass, and uttering such thoughts does not constitute disbelief. When you feel pessimistic, hold your tongue and busy it with the remembrance of Allah, and say: "O Allah, there is no good except Your good, and no omen except Your omen, and no god besides You."