Will irritated c6 nerve continue to produce symptoms even though i'm on physical therapy and have taken meds?

Certainly can: Nerve irritation can be prolonged, often lasting for months or longer, even with appropriate treatment. The goal is to see a gradual decrease in pain, numbness, tingling and burning. In my experience, numbness is often the symptom to last the longest.

Possibly: Having experienced this problem myself, i can tell you that the symptoms can go away with treatment. The etiology of the injury, such as a slipped disc , arthritis, spurring etc, must be addressed to prevent recurrence, which may or may not be possible.