I have arthritis in my knees, I am 21 years old, exercise regularly (including bootcamp twice/wk) I don't want to take tylenol (acetaminophen). Advice?

Arthritis in knees. Are you sure you have arthritis or do you mean pain? Arthritis is unusual in a 21 year old unless you had an injury to the knee. Most knee pain in young people is treatable and you may want to see your doctor to get the correct diagnosis. It could be runners knee which is treated by quadriceps strengthening exercises which are essentially strait leg raises with some weight on your ankles.
Doubt arthritis. You are too young to have arthritis- if you have crunching under your knee caps, that is very common. If it does not respond to NSAIDs (ibuprofen) and PT then see a specialist - on rare occasions at your age, surgery can help.