First of all you should get detailed investigation to know the exact cuse of vocal cord palsy. This included CT scan of head, neck and chest. If nothing wrong comes it is supposed to be idiopathic that means no cause detected.
Next Steps
There is no medicine to improve your voice. Voice therapy is the only treatment. You can wait till 6 months. Sometimes with voice therapy it improves in 6 months.
Health Tips
Meet a trained Voice therapist. Even after that if your voice is the same next option is phonosurgery.