I would advise against surgery at your age. What is the likelihood that your parents will agree to and fund it? Additionally, your face can continue to undergo changes in the next few years. My major questions are whether you are getting enough sleep and whether you smoke? Smoking can contribute to the puffiness as can lack of sleep. We know that teens need an enormous amount of sleep but tend to burn the candle at both ends.
In general, I recommend a conservative approach to all lower lids. It is an area of the face which is extremely unforgiving when surgery is too aggressive. I agree with the other respondents that a hyaluronic acid filler like restylane may be a good option in a case like yours, not only does it gently correct the depression but it is 100% reversible if you don't like it. There are still risks to injectable fillers and you will need parental consent. You also need to see some one with experience in injecting this area. But I have to agree you are not a surgical candidate, not because of your age but because surgery will not correct what is bothering you. And your face is going to continue to mature, most people would kill for your look!
Best of luck to you, in the meantime, try one of the lumenizing lower eyelid highlighters like touch éclat by Yves St Laurent or high beam by benefit. They both work wonders for this sort of camouflage.
Dark circles are usually due to relative hollowness of the lower eyelids (tear trough area), not allergies or skin darkening. Sometimes, there is excess puffiness (fat prolapse), in which case removing or repositioning the fat (lower blepharoplasty) is the answer. At times, there is true hollowness without excess fat, in which case lower blepharoplasty only worsens the situation; in this case, filler injection is the correct treatment. In your case, filler injection is the correct answer. See an oculoplastic specialist.
Your issue is related to the shape of your orbital rim. It rolls back to the orbit creating a slight deficiency in support for the lower eyelid. This causes an early demarcation between the cheek and the lower eyelid. Removing lower eyelid fat which is primarily what lower blepharoplasty is about will actually make your appearance worse. I have had very good success in filling these with Restylane. The treatment can last a couple of years for someone your age. You do need parental consent for treatment. In your area, I recommend Dr. Michael McCraken. Remember that you are beautiful. We are really talking about a treatment that will further enhance your appearance. Less is more.
A 16 year old would need consent from a parent to have any surgery, including lower blepharoplasty. I would not recommend that you have any surgery at this point however, as your appearance could still change as you mature. Sometimes a filler can be used to camouflage puffiness and improve dark circles under the eyes. I would consider this option before any surgery at your age.
You would need parental permission. But first you need complete sinus workup.. And I might try a HA filler before surgery.