When can I take more Tylenol after stopping after it for the directions of take it only for 10 days?

Usually the 10 day rule applies only when self medicating. If your physician has told you to take the Tylenol just ignore the 10 day instruction. Usually, I think, it states something like taking for only 10 days unless using under a doctors supervision or something along that line. The makers of the medicine do not want people to hurt themselves by self medicating and becoming toxic or having something that needs a Drs supervision. It is just a disclaimer for legal reasons, mainly. Tylenol is not without side effects and can be very damaging to the liver if used improperly. If you have not consulted a health care provider about your arthritis, you should do so and ask him/her about taking Tylenol on a regular basis. Two Tylenol per day is a pretty safe dose if you have a healthy liver and you do not consume alcohol. Tylenol is not an anti-inflammatory, however, and you may get better relief from an anti-inflammatory medicine since arthritis is an inflammatory response causing joint swelling and pain. Anti-inflammatory medicines can be much harder on the stomach though. This is something your physician can determine. Great job on adhering to directions! That is very important and not everybody does it. It shows you are a smart consumer and are being proactive with your health and that is fantastic!

No, arthritis does not go away in 10 days!
Have you been prescribed the Tylenol? If so you have probably been told to take it when needed. In this case ignore the 10 day warning and take it when needed, be sure not to exceed the maximum dose of 4 grams a day.
If you have not been prescribed Tylenol you should see your doctor. You will probably need to take on going pain relief. Your doctor will be able to decide what long term pain relief is going to be right for you.
https://www.drugs.com/arthritis.html