I am really bothered by the bags and dark circles under my eyes and the shape of my mouth. (Photos)

I see your areas of concern. I would suggest a formal consultation for dermal fillers and Dysport/Botox. Best wishes. Dr. Aldo

For the bags and hollowness (dark circles) under your eyes, the best long-term treatment is transconjunctival lower blepharoplasty with repositioning of the fat bags to the hollow area. 

Under eye bags and circless can be permanently corrected with surgery or temporarily camouflaged with fillers.There are great non-surgical options to fill in under eye depressions and hollowness. Using dermal fillers, a liquid eye-lift can be performed. A dermal filler such as Restylane would be placed in the cheek and tear trough to hide the depression or bag underneath your eye.
Surgery would require a fat-repositioning lower lid blepharoplasty. In this surgical procedure, fat from the eye area is moved into the tear trough depression filling the actual depression. Lip augmentations with fillers is a great option to improve the fullness, suppleness and symmetry of the lips. I prefer to use a micro cannula to inject the lips to prevent bruising. Look for a cosmetic dermatologist or plastic surgeon who is an expert in fillers. 
I hope this helps.

A combination approach will give the most improvement. Fillers, lasers, and microneedling/PRP can improve under the eyes. These lip fillers (Volbella, Restylane, Juvederm) are good for creating a symmetrical and full lip. Nova threads can be used to improve lift and shape. Implants or fat are alternatives. I recommend getting a formal evaluation with a facial sculpting expert to go over your desired results. Best, Dr. Emer

It's best to see you in consultation to discuss your specific anatomy and possible solutions.  However, lower "eye" bags and dark circles can be caused by many factors.  In many patients, a lower eyelid blepharoplasty to remove the herniating fat pads ("bags") helps smooth the lid-cheek junction.  The darkness of sometimes caused by shadowing from the "bags."  However, the skin in this area is also thinner and can take on a darker appearance.  Often we treatment the overlying skin of the lower lids with a chemical peel or laser.  As an alternative to surgery, dermal fillers such as Juvederm can be injected along the infraorbital rim which helps camouflage the "bags."  While this is not the same as during surgery, the fillers often give nice improvement until a patient is ready for a more permanent procedure.  

There are options available depending on your goals.  Fillers can be used to help disguise under eye irregularities.  Surgery called a lower blepaharoplasty will provide the most permanent results.  Another option is ALMI.  This non surgical procedure uses your own tissue to improve contours.  It also addresses the quality of skin tone and texture.

Hi Amkey84,For your tear trough concerns, you can opt for a blepharoplasty and lasers (eg. Lumenis M22) to remove the discoloration. Temporary measures would be to use a filler like Restylane Refyne. It looks natural and produces the least swelling.As for the mouth - you have an overbite which probably contributes to your problem and a slightly gummy smile. For the latter, you can use Botox. Fillers can correct the shape and add fullness.All the best, Justin Harper, M.D.