Will a Filler or Belpharoplasty Fix my Under Eye Bags?

It is difficult to judge from your photograph how puffy your eyelids are and assess the reason for your "purple crescent". If your lower eyelid has a mild bag, then a filler injected inferiorly to it (below) may hide the problem and improve any darkness caused by a shadow. If the bulging is more substantial, then the fat should be removed by blepharoplasty. Irregular pigmentation of the skin can be removed at the same time with an Erbium laser to achieve an overall enhanced appearance. All the best.

You may want to begin with trying filler.  It works to disguise under eye irregularities.  It works well in conjunction with other treatments such as chemical peels or microneedling which can address tone and texture issues.  Visit with an expert injector near you to learn more.

Bags under the lower eyelids are usually caused by displaced fat, redundant muscle, redundant skin, or sometimes even a prominent vascular plexus giving the aesthetics of lower lid bags or dark circles.
Early volume loss in your upper cheek and tear trough area can exacerbate even a small amount of genetic predisposition to having eye bags. There are numerous, good options to address this issue ranging from nonsurgical to surgical.
It is important to realize that it is displacement of fat, NOT excess fat that can cause lower lid bags. Old school blepharoplasty approach took skin and fat out of the lower lids by cutting right through the skin, which gave long term poor results with hollowed out lower lids and more potential for surgical complications. 
We know that we tend to lose fat as we age in our face, so taking more out as part of a surgical procedure may look good immediately, but it is a long term bad idea. Newer approaches to lower lid blepharoplasty do not cut through the skin and leave no external scars, this is called the transconjunctival approach. More important yet, the existing fat is repositioned instead of removed, giving much better long term results with a more conservative surgical technique that also has lower potential for complications. 
Nonsurgical options include strategically placed volume to replace early loss, which can have a dramatic impact on the appearance of eye bags and the junction between your eyelids and cheek. Volume can come in the form of fillers or as micro fat grafting. 
To ensure you are receiving the highest level of care, seek out a modernly trained, new-school dermatologic surgeon, oculoplastic surgeon, facial plastic surgeon or plastic surgeon who is board certified and fellowship trained in one of these “core four” cosmetic specialties. Membership in organizations like the American Academy of Facial Plastic and Reconstructive Surgery help to identify a highly trained surgeon.
Cameron Chesnut
#realself500 Physician