The difference between "must" and "have to" is quite subtle. We could use "must" when the obligation comes from us, we could use "have to" when the obligation depends on external factors. For example: I must polish my boots once a week. ( This is my responsibility ).
If I join the army, I will have to polish my boots every day. ( Obligation from army ).
Your sentence : "I have to go now because I am already late for my class". (Obligation from your college ).
