What can I do about these fat pads under my eyes?! (Photos)

Thank you for your photos and questions.  I think you would find a nice improvement with fillers.  They work to disguise irregularities in the contour under the eye.  Another non surgical option is ALMI.  In this procedure your own tissue is used to add volume to hollow areas.  It also helps improve skin tone and texture.

Under eye bags can be permanently corrected with surgery or temporarily camouflaged with fillers.There are great non-surgical options to fill in under eye depressions and hollowness. Using dermal fillers, a liquid eye-lift can be performed. A dermal filler such as Restylane would be placed in the cheek and tear trough to hide the depression or bag underneath your eye.
Surgery would require a fat-repositioning lower lid blepharoplasty. In this surgical procedure, fat from the eye area is moved into the tear trough depression filling the actual depression. Cost will vary and can be discussed at your consultation.
I hope this helps!

You have under eye orbital fat bags. The best long-term treatment is transconjunctival lower blepharoplasty with fat repositioning. It is important to maintain normal eye shape and function and not to get sunken hollow eyes after.