There is no replacement for an actual consultation. It is important to find a surgeon who actually is accomplished in performing this surgery. Generally this will be someone who devotes a good deal of their practice to performing eyelid and eyelid reconstructive surgery. The surgeon's ethnic identity is less important than their skills, training, and experience.
What you are describing is a situation where one eyelid has a crease and a double fold but the fold is held high with a large amount of eyelid platform show. The other eyelid does not have a crease and is a single fold eyelid. Generally, the crease forms with attachments between the levator aponeurosis and the skin. This defines a double fold. When these attachments are not present, the crease and double fold are not present. Double fold surgery is a type of specialized anchor blepharoplasty. In is incumbent upon the surgeon to precisely measure where the crease should be and to expose the levator aponeurosis. Non-oculoplastic surgeons are generally not properly trained to identify these tissue planes.
Additionally, I believe that you are describing the presence of a compensatory brow lift that may be caused by upper eyelid ptosis. This might account for some of the marked asymmetry between the two eyelids. This question would be immediately resolved with access to your photographs or more ideally a personal consultation. I would encourage you to carefully assess the credentials of your surgeon. Regarding the setting for surgery, it is essential that you are awake for this surgery because the surgeon must monitor the effect of surgical manipulations. This requires the ability to open and close the eyes during the procedure. Because conscious sedation is utilized, this, like so much surgery we perform, is done on an outpatient basis. Due to persistent swelling in the eyelid, the newly formed crease may look high for many weeks until the eyelids have healed sufficiently.