If the small fat pockets at the corners of my eyes are removed, will the under eye area looks smoother and better? (photo)

Hello and thanks for the question.  It does appear to me that you have some residual excess fat pads.  This does happen on occasion and can be corrected with a revision surgery.  I would recommend waiting a bit longer to treat this problem.  I would not recommend fillers in this area.  

When doing a lower eyelid blepharoplasty, the orbital fat is either trimmed or repositioned.  When done transconjunctivally the temporal fat pad can be hard to get to.  So sometimes this pad will be under-resected and you will end up with the appearance you have with a prolapsed fat pad.  This can be removed with transconjunctivally or via a skin approach.  Usually best to wait until 6 months post-op but you are almost at that point now.   

Thank you for your pictures. Unfortunately, you have had under resection of your lateral fat pads. These fat pads need to be treated aggressively to produce a nice contour. You will need repeat removal of this fat pad. 

If you had a lower eyelid blepharoplasty with removal of loose skin, but no treatment of the fat, then the fat pockets can certainly be more apparent afterwards. In general, it is reasonable to wait at least 6 months to allow any swelling to resolve before considering further treatment.Filler can definitely be used along the tear trough/orbital rim to help improve the hollowing and camouflage the fullness of the fat pads. This is a relatively straightforward procedure with little recovery time and lasting results. However, if the fullness persists, then a revision lower eyelid surgery may be done with repositioning of the fat pads in the inside and middle of the eyelid and conservative removal of the fat pad in the outside corners.

It looks like you still have the lateral fat pad. This can be treated by a repeat procedure in many different ways. Fillers canhelp the tear trough region.

My question back to you is 'why was not the fat compartments of the lower lids partially removed?' So you would not have this issue...

A lower lid blephroplasty includes removal of the excess peri orbital fat which causes bulges at the corners of your eyes. I would wait until you are at least six months post op and then consider a trans conjunctival removal of the excess fat and release of the arcus marginalis which causes the crease below the fat. This would allow some of the excess fat to slip below and soften the transition from you eye to your check.At the same time, I would recommend fat grafting the check area and other areas if indicated. Fat grafting if done correctly results in 60-80 % take and is usually permanent.