Dark circles under eye circles were not improved by filler: what next? How soon after filler can I do carboxytherapy? (photo)

There are many things you can do to treat under eye bags, but a combination approach with nonsurgical treatments would give the most improvement: fillers (Belotero, Juvederm Volbella), lasers (Fraxel/CO2), Renuvion (J-Plasma), microneedling/PRP, Cosmelan peels and stem cells. A surgical option to remove skin and/or fat might be the best solution long-term. I suggest getting a formal evaluation with a cosmetic dermatologist to see what is best for you and your goals. Best, Dr. Emer.

Placing filler into the cheek will often help with the appearance of the tear trough.  You do not have a very deep trough in these pictures, but still have some after the cheek filler.  Have them place some filler into the area of the tear trough and you should note an improvement.  It shouldn't take much filler to do this.      

The wonderful thing about fillers is that they work well when combined with other treatments for a more complete result.  You can consider laser treatments, chemical peels, and microneedling to help improve the overall area.  See an expert in your area for an evaluation and discussion of proper treatments for you.

Your photos show that you have tear troughs.  These can usually be treated with a filler into the tear trough.  While many injectors will inject the cheeks attempting to correct problems like the tear trough, this approach often fails as the filler is too far from the problem.  The other concern that many injectors of products like Juvederm or its cousins like Vobella is that they are worried about creating a blue hue or Tyndall effect.  For this reason, I like using Bellafill which will last at least 5 year and does not cause these problems as you can right in the tear trough and get great results.
I hope that helps.  I have added a web reference to many before and after photos of exactly what your concern is.

I hope that helps.

Best regards.