I Am 20 and Have Enormous Puffy Bags Under my Eyes. What Kind of Surgery Should I Get?

Thank you for your question about eye bags treatment.  Fillers are often an excellent choice for the treatment of this area, but filler only camouflage the appearance of these bags...and eventually surgical intervention may be necessary.  It is vital that you are seeing a seasoned professional for this area of the face.  If the filler is placed incorrectly it can make the prominent eye bags even worse.  The use of a cannula in this area can minimize bruising and the risk for vascular compromise.  
To be sure, see two or more experienced, licensed and board-certified providers in your area for a complete evaluation to make sure you are a good candidate and that it is safe for you to have treatment. I hope this helps. 

I would first start with some filler to the lower lids, namely restylane.  If this does not improve the appearance, a lower lid blepharoplasty with fat repo with a transconjunctival incision is the way I would good.  Obviously an in person consultation is needed to make any surgical decision.
Dr Z

There are many causes of eye bags. Some are shadow issues, some are discoloration issues.  Most people have a multifactorial problem meaning they have more than one issue causing this demarcation. Below is a list of common issues and my treatment protocols. 
1. Prolapsed orbital fat through the orbital septum: treated with lower lid blepharoplasty and fat transpositioning. Can also be helped with fillers or auto fat transfer to the face but the ideal treatment in my hands is surgery for this issue.
2. Eczema: much more common in young people with fair skin. The treatment for this is to hold off on makeup and any manipulation of the lower lid for a few weeks and try some topical anti inflammatory creams. If you have allergies those should be treated also.  A dermatologist is the best person to see for this. We have a multidisciplinary clinic with myself, a plastic surgeon, and my partner, a dermatologist which I think is ideal!
3. Fluid accumulation and/or redundant skin. Could be possible in young patients but would need a good facial analysis and exam to determine. A low salt diet (< 1000mg/day) and a warm compress can help.  I would consider treating with filler/fat transfer, lower lid fractional ablative laser and/or lower lid blepharoplasty.
4. Descent of midface cheek pad. This then causes the nasojugular ligament to become more prominent creating a demarcation and separation of the eye from the cheek subunit. Treated with mid face lift and/or fat transfer.
It is all about the balance of this transition from the orbit to the cheek. There are many ways to treat this and they vary by the underlying cause. I recommend seeing a surgeon who also does a lot of these treatments. This can make a big difference as most people have a combination of the above that lead to the issue.
Hope this helps.
Best of luck,
DrC