Post-operative asymmetry is dependent on many things, most importantly, the presence and nature of asymmetry pre-op. It is most common and natural to have some asymmetry of the breasts, and this can be related to size, dimension, chest wall (i.e.ribs and muscle), degree and location of laxity or sagging, position of nipple relative to breast and relative to your chest, presence of scoliosis, etc.
It is also very common for breast implants to sit asymmetrically once implanted by the very nature of the anatomical dissection and the unknown and uncontrollable factors of tissue relaxation, capsular contractures, and gravity Some asymmetries can be improved, some will be worsened, and some will require trade-off (for example, making breast mounds symmetric in size and location at the price of asymmetry in nipple position.
The reason why you have asymmetry can only be determined by examining you pre-operatively to see what you began with. That will help a discerning surgeon to determne why you are asymmetric now and whether this will improve with time and/or require surgical correction or require you to accept imperfections in your result.
If you had a fuller but tigher left breast and a more saggy loose right breast, that might explain your relative roundness and fullness on the left and your rippling on the right with the lower nipple position. In any case, it would pay to wait until the tissue accommodate the implant possibly 3-6 months before contemplating any revision. I suppect that you will always have to fight some asymmetry.