What is the fat bulging from the outer corner of my eye? (Photo)

They are two different surgeries. Blepharoplasty only correct the excess skin over the eyelids and it may even correct the fullness over the eyelid with removal of fat from the eyelids. Ptosis is correction of droopy upper eyelids and opening of the eyelids. It has to do with the eye muscles and...

I doubt the crying had any real effect on the healing.  However, you don't really state what about your eyelid surgery you didn't like.

 I think the appearance of your eyes are normal and look nice. This is great news because it is not something that can be easily adjusted with surgery. Therefore it would not be recommended. 

A current CT scan can be very helpful to determine what is going on in the orbit.  It is always possible that tissue was entrapped in the back of the orbit when the implant was placed.  That is a common issue even when very "expereinced" surgeons do the work.  It is just very...

Your eyes look beautiful and symmetrical.  I can't think of any way to improve them.  You have been born with excellent anatomy so be careful about altering it as any alteration may not maintain the same smooth shape and balance.

Everyone has slight asymmetries in their body and potentially the orbicularis muscle is stronger on one side.  I wouldn't do anything surgical.  If this bothers you, consider Botox or Dysport with an Oculoplastic Surgeon.