What can I do to address this shadowy area in the tear trough corner? (Photos)

I highly recommend against filler in the periorbital area. If it is not done correctly, it can create a lot of problems (especially in the wrong hands). I would recommend facial fat grafting if you truly wish to increase volume in this area. I would recommend seeing a board certified plastic surgeon (American Board of Plastic Surgery) with extensive facial surgery experience.

The under eye skin is very thin and is not forgiving when it comes to excessive under eye filler. Based on your photos, it's not clear what you were looking to achieve. This is probably why your doctor does not wish to inject you. I wish I could be more helpful. Sincerely, Dr. Joseph

Even with your drawing, I am literally moving my head around to try to see what you are talking about. If you're talking about the horizontal line under your eyelashes, this is due to the tarsus of your lower lid and will always be there and possibly become more noticeable as your skin thins above it. Beyond that, I don't see any hollowing. Leave it alone.