Will my facial nerve damage after tear trough filler subside? What should I do next?

It appears you did suffer a nerve injury due to the cannula going a bit too deep and low. The nerves may heal themselves over time. However, you may want to consult with a board-certified physician with experience in nerve injuries to see if treatment could be performed to speed the healing process. 

What you had was an injury of the infraorbital nerve and artery as they come out from the bone. Injury to these can occur if the canula or needle is placed a little low as they emerge at about the level of the top of the nasal alar flare. Frequently, as the nerve grows back, the nerve fibers are not in the same place they were so the sensory impulses get mixed up. Since the brain does not recognize the signal, it frequently interprets it as pain. The usual treatment is to determine what causes the pain and then multiple times a day repeat the stimulus, both on the injured side and the opposite side, telling the brain they are the same. After a while, use things with different feels to see if you can tell what it is on the right side without looking. Eventually, it all gets better. This is called desensitization and sensibility reeducation. If you think you need help, see a plastic surgeon with experience with hand surgery, as nerve injuries are very common there.