If you suddenly stopped taking an antiinflammatory, could that make arthritis worse?

No: Stopping an anti-inflammatory medication will make the symptoms worsen but the arthritic condition will not change. In rheumatoid arthritis, drugs that change the condition are called disease-modifying anti-rheumatic drugs (DMARDs). Some arthritic conditions can have the natural history or progression altered. Some arthritic conditions such as osteoarthritis have no proven disease-modifying drugs.