I am a 21 years old widow with a 1-year-old son. Is it compulsory for me to get married or I can live as a widow through out my life? May Allah (SWT) guide us to the right path.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Allah has permitted you to remarry after the end of your waiting period (Iddah).  It could be that you must get married if you fear falling into Haram (illicit sexual intercourse), or other sins.

Allah knows best.