Hi Natalie Martinkus,
Could it be that your shapefile does contain geometry (points), but these points do not show up where you expect them to be?
Test:
Could you please double-click on one of the records in your attribute table to zoom in to it on the map? What happens now? Do you see a point on the map? Where is it located?
Questions:
Which desktop application are you using, ArcGIS ArcMap or ArcGIS Pro? And why are you downloading your data to a shapefile first, instead of accessing the Feature Layer directly from within your desktop application?
BR,
Egge-Jan