It is possible to get some temporary discoloration of the skin after a CoolSculpting treatment. Sometimes, this can be bruising, but it is also possible to get redness or a pink discoloration. If discoloration occurs, it is not always on both sides or the same on both sides, so it would not be unusual for you to have one flank slightly pink and not the other.
Each treatment area is different and can have different reactions. You really can't compare different CoolSculpting areas. As long as you did the full treatment, there is no need to worry.