Is arthritis curable? How would you know when you have arthritis and what type do you have?

No. Arthritis is essentially degeneration of the cartilage of a joint, it really isnt "curable". However, there are things that can be done to slow the progression of joint wear...And there are also ways to alleviate the pain that is associated with this disease. Most arthritis is degenerative, there are other types that are autoimmune such as rheumatoid but much less common.
See a rheumatologist. There are many forms of arthritis that needs to be evaluated by a rheumatologist.