Is what is happening, in terms of the obstruction of my marriage to this young man, an ill omen—as some say—and must I perform the Istikhara prayer or not?

The fears people raise about your engagement and delayed marriage are unfounded and fall under the forbidden ill-omen. As for Istikhara (prayer for guidance), it is prescribed for every permissible matter. Its completion lies in abandoning one's own choice and entrusting the matter to Allah after emptying the heart of all thoughts. The preponderant view is that one should proceed with the matter after performing Istikhara; for if it is good, Allah will facilitate it, and if it is bad, He will avert it.