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It is correect to say I am going to the party or is it correct to say I am coming to the party? My understanding is the person at the party says "are you coming to the party?" and I would say yes, I am going to the party. Not I am coming to the party.
Either is okay.

You can say "I am coming to the party" or "I am going to the party". The former implies that the party is imminent, or that you are talking to the party's host.

Except I never get invited to any parties!
I think you'd tend to "echo" the verb if you are responding to a question. The person throwing a party would say "are you coming?" so you reply "yes I'm coming"

and a fellow guest would ask if you planned to go, and you'd say "yes, I'm going"
Here is one of the safest way to distinguish the use of "go" and "come."

If you, as a speaker or listener, are moving to the other party engaged in communination with you one way or another, you are definitely "coming." If the other party, as a speaker or listener, is moving to you in the same situation mentioned above, he is also "coming." In all other cases, you are "going" because you have unilateral destinations by yourself.
This leads to the following thought when would you say: Am I coming?
Only if you were incapable of making your own decisions, otherwise you would already know (or at least, have more knowledge about what you might choose than the person you're asking). You might ask "Am I invited?" though.