I damaged my under eye skin with Hyaluronidase. What can I do to regain elasticity and thickness? (photo)

Hyaluronidase does not damage normal skin.  The pH of the solution is not at the right pH to damage normal elastic or collagen fibers or any natural hyaluronic acid.  I suggest co2 laser in combination with PRP and radiofrequency laser treatments to improve the under eye.  The goal is improvement, there is no "cure" or reversal for aging of the under eye.  Fillers appropriately placed with cannulas can also help if done by an expert.  Best, Dr. Emer.

My feeling is that the sagging skin in due to the excess
volume created by the filler and hyaluronidase and this has caused the skin to
stretch. Thus is not from the hyaluronidase but rather the volume of fluid in
the area stretching the skin. This unfortunately may take months to tighten up
or you may need a procedure to tighten it. 

There are a few options that I can suggest to improve your
condition. A retinol based eye cream is great option. Options include:

-ZO® Olluminate Eye Repair

-ZO® HydrafirmT

-SkinCeuticals® AOX Eye Gel

Other options include botox injection into the lower eyelid.
Filler is not likely going to fix the problem and might make it worse. Surgery
for excessive buldging might be an option as well. Skin resurfacing
procedures (laser resurfacing with CO2 laser, Er:YAG laser, Fraxel DUAL®,
PicoSure® FOCUS Lens Array or OBAGI® controlled depth chemical peel) might be
an option. This is an advanced technique so be sure to get an experienced
dermatologist or plastic surgeon consultation for recommendations and treatment
options.