People who live away from your families, how do you cope with the distance?

I(23M) have moved to a different country for higher education, moving away and living alone for the first time ever. I have lived with my family ever since I was a child. When I was leaving and my family came to see me off at the airport, I didn't cry, not a single tear. But now when I'm here, alone, I get these short pangs of intense longing. Certain songs and memories sometimes make me cry uncontrollably. I cannot tell this to my parents because they would worry about me being alone.

Has this happened to anyone?