If you use the default Join Operation, the output should contain a field, Join_Count, which tells you how many are found/matched.
If you use the JOIN_ONE_TO_MANY option, the output will contain multiple records for the same point, one for each match found. You can then use the Frequency tool (Analysis toolbox - Statistics toolset) with the target point features FID field as the Frequency Field. The resulting table contains the count for each unique FID.
Could you describe why or how using JOIN_ONE_TO_ONE didn't work for you? Did you get an output? Did the output have a field named Join_Count?
About the frequency output table, I understand it is a table, no features. I suggested that you try Join Field tool (Data Management toolbox - Joins toolset). You should specify the following:
Input Table - specify your points (the shapefile)
Input Join Field - Select FID
Join Table - specify the output table of Frequency
Output Join Field - select the FID field
Join Fields (optional) - check the box labeled FREQUENCY
Click OK to run the Join Field tool. This process transfers the FREQUENCY field from the output table of Frequency to the point shapefile. You can now right-click the point layer, go to the Layer Properties - Labels to label the FREQUENCY field; this is the count you wanted. Does it work?