I'm upset with my friend for not inviting me
What did they not invite you to?
They threw a party and I was not invited.
It is ok to be upset at that. You should ask why you were not invited so you know for next time.
You should not have to beg to be invited to a party. I'm going to break their confidence down and make sure that they never invite me to anything again.
Being upset is fine, but there is no reason to do the things you outlined here. Just talk to them normally about why. Maybe they just forgot to.