Wash the limes. Cut both ends off lime to remove nubs. Slice 3 of the limes into 8 sections.
Place the sectioned limes in a blender. Pour in the water, rum, coconut water, sugar, and sweetened condensed milk. Blend for 2 minutes, or until limes have broken up into small pieces.
Strain the chunks through a fine meshed sieve into a bowl. Rinse out the blender and return the strained mixture to the blender. Add the ice and blend until frosty. Serve with a lime wedge.