Hello Angela,
Based on the research I've done thus far it there doesn't seem to be built-in Spatial Query functionality. There is a thread for this on the ArcGIS Ideas page though. I would recommend up voting this idea in an effort to grant it additional traction.
https://community.esri.com/ideas/1426
A lot of the workarounds I've found to achieve this functionality involve custom scripts which can become complicated depending on your level of expertise. However, being that you are just trying to display point features within a certain polygon boundary, there is an easy and straight forward method that allows you to do this. All you need to do is go into the 'Map Properties' > 'Clip Layers' > 'Clip to the outline of features' > Specify polygon feature class. Then go down to 'Exclude layers from clipping' and check everything except for the point feature class that you want to be within the polygons.
I hope this helps!
Lukas