Can I show up to hang out with friends even though I wasn't invited?
Why are you going to show up uninvited?
I hate my friends for keeping me out and I want to make them feel guilty by showing up
You should talk to them first. Maybe there is a good reason and you just don't know it.
I figured this is an opportunity for me to be an asshole and show my friends how much I hate them.
It doesn't sound like you hate them, but are instead just hurt that they didn't invite you which is completely fair. However, you should let them know later that you were hurt and not crash their party-- otherwise you're just proving them right to keep you away.