I'm going to tell my father that he embarrasses me in front of the people at my school
Has he done that in the past?
Yes, when I was in middle school.
It is good to communicate with your father about things he does that embarrass you. He might not know he is doing it and will stop when you say so.
I hope he does, I am a bit tired of it.
Don't expect him to change instantly. It takes time to correct and change behavior of people. Letting him know is the first step.