Update 12/18/2016 - Orlando International Airport as of 12/18/16 has only one official nursing mothers room and it is located past security at terminal A.
Mom Katie B. shared this photo of Orlando International's new nursing room. We will add more pics soon, and more info about the amenities.
Photo credit: Mom Katie Bowman
Last resort option:
There's a Family Companion Room (Companion Care Restrooms) located on Levels 1 and 3 of the "A" and "B" Terminals and at all four (4) Airsides (gate areas). However one nursing mom reported on December 18 2016 that it was extremely dirty and disgusting to use
We contacted Orlando Airport Information and they told us the information desk is more than willing to help nursing mothers find a more private and quiet spot to breastfeed or breast pump when they need to.