I have puffiness under my left eye only. What could be the cause of it and how can I get rid of it? (Photo)

Do you sleep on your left side? This could be part of the issue. If so, make sure that your pillow elevates your neck enough so that it's in line with your spine. The fact that it itches leads me to believe that there may be an allergy going on. I would suggest that you make an appointment with your physician to have it assessed. 
My best,
Dr. Sheila Nazarian
@drsheilanazarian on Instagram

You may want to talk to a doctor to see if fillers may work for you. Maybe talk to them about Belotero, or what other fillers they recommend. this is something that you do not need surgery for unless it is necessary. Lower Blephs. The price for surgery starts at $3,500.

You are noticing the lateral fat pad in the left lower lid.  This is a normal fat pad, which has moved forward a bit so that you can see it.  In the morning it will often be more noticeable.  Not much to do for this unless you have it surgically removed.  If it doesn't bother you, just wait.    

Since your eyelid puffiness is greater in the morning, there is a fluid component which could be vascular or lymphatic.  Often one eye is affected more than the other when the patient sleeps on that side.  The itch also suggests there could be an allergic or eczema component.  Make sure you have seen your internist to confirm that you have no underlying issues that could lead to swelling.  If the itch persists, see your dermatologist for treatment.  If everything else is normal, then you can return to your dermatologist to see if a combination of skin tightening and fillers can reduce your asymmetry.  However it is important to note that neither will change your eyelid being puffier in the morning.  And if there are fluid issues, adding a hyaluronic acid filler, which absorbs fluid, could make it worse.I hope this answer is helpful.Wishing you the best of luck.

Normally, we have three fat pads under the eyes which work to provide support to the eyelids and socket.  The fat pad closest to your ear (known as the lateral fat pad) seems to be protruding a bit.  This is often the result of aging, but can also be related to way you sleep or other more rare medical conditions.  Start by making an appointment with an oculoplastic surgeon to examine your eyes and discuss the treatment options.  Good luck!