My mother, grandmother and great grandmother all had terrible bags under their eyes. I started getting them in my late 30's. They were worse when I drank wine in the evening or when I had sinus congestion.
I've done a number of things to improve my health, and my undereye bags are nearly gone. Just little nubs remain, high on my cheekbones. I hope they will go in time. Even my daughter has commented how much better my eyes are looking. She was looking at them with an eye to her own appearance 30 years from now.
Things that may have contributed to the improvment:
1) MSM and Vitamin C - that was the first thing I did and it helped. My liver enzymes were raised in the begining, so I think the MSM caused a detox. They went back to normal after a while. I ran out of MSM and haven't taken any for a year or so. I think MSM and NAC (below) are redundant, but NAC is better.
2) N-acytle cysteine, Vitamin C and alpha lipoic acid. I wouldn't do without that combo. It is an antioxidant blend. NAC is an amino acid, a precursor needed for the liver to generate glutathione. I really notice my energy level improve when I'm taking it regularly. If I have wine in the evening, I'll take an extra dose of NAC, vit C and alpha lipoic acid to keep from puffing up in the morning.
3) Coconut oil on my skin. I use this regularly after my morning shower. In the beginning, it made my skin feel rough and very dry. This took several weeks to pass. I think the coconut oil sloughed off the skin layers damaged by the mineral oil based products I had been using. I put an herbal gel moisturizer over the oil after it has mostly absorbed. My skin is now baby soft, more translucent, with less apparent sun damage on my cheek bones. Best of all, my "smile" lines have lessened.
4) Liver flushing. I started this later, after the bags were reduced. It lessened the dark hollows under my eyes. When shadows recur, I know it is time for another flush.
5) More excercize. Improving circulation and lymph flow, excercize helps keep the fluids from stagnating. It also helps me sleep better. I've also been doing inverted yoga postures, which increases circulation to the head.
Let us know what, if anything, works for you!