LOL, I had severely impacted teeth and it was a breeze. OK, there were a few discomforts, but overall it was smooth even with complications.
IMO, The small amount of discomfort is nothing compared to the torture you've put yourself through.... Seriously, just do it.
You are not being a "pussy", you just got a Pavlovian or conditioned response stuck in your head. After the first few times of backing out due to anxiety, you formed a "habit" of sorts in your brain. It is an automated response now. You can break the response by going through with the procedure. Don't let the anxiety of the conditioned response psyche you out.
Conditioned responses can be good if they benefit us, but gone awry like this one, they can really screw with your life. Realize that you brain just got stuck in a bad loop and you need to break that loop. Get the teeth pulled, you'll be glad you did it for more reasons than one.
P.S. I had my gums cut (all four) and did not need any pain killers beyond Ibuprofen. You could very well do the same.
I hope this helps....