When someone "comes up to" you, it means that they come close to you that they can talk to you. For example:

After my lecture, a student came up to me and told me about a dumb mistake I had made.

You use "come up to" when a person comes to you. But what if you are the one who's speaking? The phrase for this is "go up to":

I went up to the professor after his lecture and pointed out that he had made a mistake on one of the problems.

Another word for this is "approach (someone)". But "approach" is a more formal word.