A third eyelid procedure is risky. Repeat external incisions can weaken the support of the lower eyelid and cause an ectropion or sad eyed look.
You need to be examined by an expert eyelid surgeon who can asses your lower eyelid support.
If you have good eyelid support and good eyelid closure then an operation on the inside portion of the eyelid, called a transconjunctival blepharoplasty may be possible. During this procedure, composite (whole) fat grafts can be harvested form the tummy and inserted into the lid to plump the dark circle.
Avoid filler injections or injection of fat through a needle, the risk of visible lumps, scarring and injury are too great, especially since you have had previous surgery.
I do not know of a surgeon in Asia who uses this technique.You will have to seek recommendations from your doctor.
See before and after photos of Fat Grafting.