Would filler fix my deep set eyes? (Photo)

You have beautiful skin and a pretty face.  Fillers can be used to help address the under eye concerns that you mentioned.  Fillers work by disguising under eye irregularities.  The treatment is done in the office and the results last up to one year.  See an expert injector in your area to learn more.

Dark under eye circles can make you look tired and older than you are. I would use a combination protocol that includes topical Melarase creams first, followed by a combination of injectable fillers, fractional laser, and RF to blend out the eyelid hollowness and tighten the skin. 
Recommended Creams: Melarase Brightening Kit
MelaClenz
Melarase AM
Melarase PM
Melapads
Replenish Retinoid Cream
Best, 
Dr. Karamanoukian
Realself100 Surgeon

Under eye hollows can be permanently corrected with surgery or temporarily camouflaged with fillers (Restylane, Belotero, Volbella).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.
I hope this helps!

Your very young with excellent skin in a pretty face. Filler injections can camouflage a depression underneath the lower eyelid but will not correct deep set eyes. I honestly think you look great and would advise against taking any steps which will alter the appearance of your lower eyelids. Repeated injections of fillers can have negative effects on the eyelid skin over time.