Can I take antiviral medications to treat parasites?

No. Medications are specific to the cause. Antivirals are for virus infections, antibacterials are for bacterial infections, antifungals are for fungal infections and so on. I do not believe that your pcp or other physician would inted to treat you for a parasitic infection with an antiviral. There may be some confusion on what you have or what you are taking or there may me more to the story.