Is eye strain be caused by shortsightedness?

Usually not.: There are muscles inside the eyes that contract when near work (like reading) is being performed. Prolonged periods of such contraction can lead to eye strain and headaches; glasses can support those muscles so they don't have to work as hard. Shortsightedness, or myopia, is inablility to focus at distance. Generally things up close are in focus.

Yes: Eye strain is a physical feeling. It is usually not accompanied by anatomic eye changes. "shortsightedness " which is uncorrected by glasses can give the person feelings of strain. Not wearing glasses will not damage the eyes in a permanent way.