are tylenol 3 a narcotic

Yes, they are.

Yes. Tylenol 3 is a combination of codeine and tylenol (acetominophen). The codeine portion of it is an opiate, which is also sometimes called a narcotic, and the tylenol part is there to help the codeine work better. Tylenol 3 is a serious drug, and it can lead to addiction issues. It is one of the best pain killers on the market, but it should only be prescribed to those who really need it and its use should be carefully monitored. It's hard to come off it, and anyone who is prescribed it should know this going in. 

HTH, best of luck.