Your problem is very complex, transconjuctival blepharoplasty will remove volume, filler injection will add volume!!! as you can see, this does not make too much sense.
Neither one of these options is the best, you can get partial solutions with either. This is usually a familiar trait, most of the time patients like you also have loose skin in the lower eyelid, this can only be determined with an examination. There are 3 key components on examining your problem, excess fat (bulging bags), tear trough deformity (the groove under the fat bags) which is a volume deficiency and most likely excess skin. There are many ways to approach these problems, you need to see a surgeon with experience on blepharoplasties, there are 3 major specialties in which you can find good and bad surgeons (PLastic surgeons ABPS certified, Facial plastic surgeons, which are ENT doctors and Oculoplastic Surgeons, which are ophthalmologist) You need to see pictures from the surgeon, the best way to find out if they have experience with patients like you is if they can show you pictures of young patients like you, also is very important for you to check the lateral photographs, with this view you can check if the problem is corrected with their proposed treatment. Good luck in finding a good surgeon