I Just Had Surgery This Morning On The Joint At

I just had surgery this morning on the joint at the base of my thumb. I've had it before so I know to take my pain meds to stay ahead of the pain, but I fell asleep and didn't take them quite soon enough. Now the nerve block is wearing off. I took 20 mg oxycodone immediate release an hour and a half ago and it's still hurting a lot. Can I take Tylenol to get "caught -up" on the pain relief until the next dose. Am I correct that this medicine does not have any acetaminophen. I don't want to cause liver or kidney problems.