In some patients, filler underneath the area of the bag may smooth out the contour enough that surgery is not needed for correction. My preferred filler for this area is Restylane. Most patients will have swelling for 2-3 days, and some have bruising for up to a week or so. However, this is generally better than downtime related to surgery, and it is certainly less risky.
Many patients, however, will still have some suggestion of undereye bags after filler unless surgery is done to remove or reposition the fat that tends to herniate (or bulge) over time.