George Bush Intercontinental Airport does have a dedicated nursing mothers room in Terminal A, BUT if it's occupied or too far away from your location in the airport, you can opt to use the family restroom located in Terminal E.
This is not a dedicated nursing room because it contains a toilet, and the occasional dad/husband or older siblings might be there with moms. We don't know of comfortable seating available, but there's an outlet, changing table, and a sink.
#bfus