It is difficult from the looking up photograph to see exactly what the problem is. It appears as though there is hollowness immediately below the eyes, some retraction of the eyelids, and fullness, perhaps with irregularities from ? fat injection below that at the eye-cheek junction. It appears that your eyes are quite prominent.
Often when prominent eyes are operated on through a lower eyelid (subciliary) incision, the eyelids can pull down, as though seeking a lower position on the spherical globe (eyeball). This can present a problem visually and also functionally as the cornea becomes chronically dry.
The issue you had pointed out, however, was none of the above; rather it was the persistence of fat below the eyes. In your photo this seems to be primarily low down at the eye-cheek junction, and does not consist at all of typical lower eyelid fat that can be removed readily.
Consultations with surgeons skilled in the midface and revision lower eyelid surgery should clear this issue up further.
Although we have written many publications and chapters on your topic, we are never quick to reoperate. Any revision to lower eyelid surgery with lid retraction would typically involve midface advamcent (some type of cheeklift), plus canthopexy. Canthopexy alone can give the eye a severe look with an uptick at the corner but unaltered central roundness of the eye, a characteristic "done" look. Also, grafts such as LiveFill (nontraumatized fascial fat grafts) placed directly in regions of hollowness can help. If there is lumpiness from fat injection, this is usually removed directly.
Patients having revision lower eyelid surgery must be realistic about their outcomes, which are usually subtly better and not completely curative.