I'm so glad to hear you saw a new doctor who listened to you. I know how frustrating it can be to have a doctor who doesn't listen! I recently switched back to my pcp from my pm because of that.
I take both oxycontin & oxycodone. I just started the oxycodone a week ago. We still haven't found my maintenance dose of medication yet, so we are still playing around, but the oxycodone does help me somewhat. You are correct that the oxycodone (roxicodone) does not have tylenol in it, it is straight opiod, so your doctor will have more freedom adjusting your dose of it, as you don't have to worry about reaching the max amount of tylenol your body can take per day. However, it is supposed to last 4-6 hours, and I take it every 4 hours, but I find that it only lasts 3hrs. I take it, feel a little better, and then will suddenly feel worse. If I look at the clock when this happens, it is always between 2.5 and 3hrs of having taken the oxycodone. My doc ideally wanted me to take my next dose before the previous one wore off, but since I can't take it less than every 4hrs, that isn't possible for me. I've never heard of anyone else having the oxycodone only last 3hrs, so hopefully it will last longer for you. My body just tends to be very stubborn.
Good luck! I hope you get some better relief!