Would you apologize to someone if you knew that you made them feel upset?

[Rainbow]

When I was in high school, I remembered that I once confronted a male classmate that I have been classmates for a long time and I remembered that after I confronted him about making fun of me when I was sitting in front of him that he started to give me angry looks the end of semester 1 and throughout semester 2 when I was in the hallways. Every time I see him, I felt bad and I sent a message of apology that said, "I'm sorry if I ever made you feel upset about anything that I said or did to you." I sent the message on facebook (he didn't even accept my friend request) on the last day of highschool. Did I do the right thing or shouldn't I have not sent the letter? Thank you for taking time to answer my question.
He responded saying thank you don't even worry about it.