I'm having labeling issues in ArcMap 10.5 with lines and polygons layers created from a selection, I have not tried to label a selection of points but I'm guessing the issues is the same.
1. I select features for my map and create a layer of my selection.
2. I open the Layer Property window for the new layer that contains the selected features.
3. Under the Label tab I check 'Label features in this layer', change the Label Field and click OK.
4. The window closes and all features from the layer I selected from appear with the label I selected.
Some things I found that need to be noted about this issues/bug:
1. If I create a layer of my selections and on turn on the label but not change the Label Field everything is good to go, the layer of selected features appears as it should with 'default' label. The only work around I have is to create a Shapefile of my selection.
2. I don't have to turn labels on to have this happen, all I have to do is change the Label Field.
3. If I open the attribute table of the layer created from my selection only the selected features are in the table, but after I close the attribute table and go through the steps above all features from the source layer appear.