Both are completely correct in that context. The I am going to go to college could imply you are doing something else before you go to college in that context but doesn't have to.
The main difference between these two structures is if you are asked that question: "are you going to college?" By someone who doesn't know if you are a student or not. The two answers then imply diffrent things the first being yes I am a student. The second being no I am not a student right now but I will be in the future.