Is this a good idea for treating my knee pain?

No, they won't help. You might try an anti-inflammatory called Curamin made from turmeric root. I know some folks who stopped their prescription meds and are taking this instead. But I also know some folks who say it didn't work for them. You can find it on line or at health food/vitamin stores. If you want to stay with chemically manufactured, you might switch to Aleve rather than Tylenol. Aleve (Naproxen) used to be a prescription anti-inflammatory. Good Luck.