Is carboxitherapy effective for under eye bags? I started treatment 3 weeks ago and have seen not change. (photo)

Hi Josephine, 
YES! Carboxy therapy works well for dark circles and puffy under eye area if the problem is caused by poor circulation as that is how it works for those problems. 
Poor circulation under the eyes can be from: genetics ( you are born with it, mom or dad has it), allergies, filler in the under eye area, surgery. 
When circulation is poor the good stuff (oxygen, nutrients, enzymes for cell function) cannot get into the area well (think traffic is backed up and your car can't get where it is going). Additionally, the garbage that your cells generate gets stuck (think traffic again...your car can't get out of where it is). This combination means less healthy new cells and more damaged dying cells.....and thats why the eyes look like they do. 
Allergies cause inflammation, inflammation is swelling and impedes or overwhelms the flow of the circulation. Filler is a mechanical blocker of circulation. Genetics....you don't have great circulation in the first place. 
Injecting CO2 into the very superficial tissue around the eyes basically opens up the highways so that traffic flows. Good stuff can come in and bad stuff can flow out. It works  great, but it takes some time. Typically when clients have the puffiness, they see results fairly quickly sometimes even after the first treatment although generally it doesn't last long term yet because nothing has permanently changed in the quality of the circulation yet. So it just gets the flow going but it can't change the capacity of flow right away. Think of a highway that is always full of traffic, and really needs a new lane added to handle the capacity of all the cars that need to flow in and out of the area. 
The carboxy therapy, when done repeatedly on a weekly basis, will eventually convince the brain that it needs to start generating new healthy circulation (more lanes on the highway). That is when you should see the improvements last. Now if you have allergies, that needs to be addressed as an underlying problem that is blocking flow in order to get long term improvements that hold. Depending on the underlying issues some clients need to come in on a monthly basis, and some can hold out for years. Someone experienced in years of CO2 therapy can guide you on this depending on your particular situation. 
Treatments in my clinic are $249 a session, and we do 1x per week for about 2 months. If you are not seeing any changes (even temporary) for 4 sessions, something is not working. Either the treatment is not being done correctly or you have an underlying issue that needs addressing usually allergies. A good practitioner should rarely cause any bruising and be able to minimize it if it does happen immediately during the treatment. 
I have never seen anything else work as well for the under eyes except blepheroplasty when there is an excessive amount of loose or fat pockets, and never for dark circles. Filler is a hit or miss under the eyes and can cause more problems than it can fix. 
I hope this helps
All the best, 
Dr Jamé