Restylane Vs. Fat Grafting for Under Eye Hollows?

Restylane will last about 6-9 months but can improve this area. Fat injections can last 8-10 or more years. You are one the right track though. You need volume in this area and that's the best way to improve this area. One thing to realize is that restylane will go away and can also be taken out earlier if you wish through enzyme injections. This can be reassuring.
Fat injections are more permanent and is a little harder to get rid of if you don't like the volume but can be done through different special procedures. In my opinion, fat injections / transfer leads to the most natural results.

Both fat and Restylane can be used to fill out hollows under the eyes.  Fat has the advantage of being permanent but is a bit more unpredictable.  For those who want quick fixes with little to no downtime, Restylane is the appropriate choice.  For those who want more volume and permanent results with added downtime, fat is the better option.

Although you may have heard scary things about both procedures the incidence of them happening is quite low. That being said the potential bad things that can happen from fillers are generally less severe and usually reversible when compared to fat transfer.
You are young and your lower lid contour is relatively good. I would recommend beginning with filler. You don't burn any bridges and I beleive you will be pleased with your result.