John:
Try the new Collector for ArcGIS app (10.2.2).
https://play.google.com/store/apps/details?id=com.esri.arcgis.collector
Then, at a browser on a computer, load your zipped shapefile into your My Content area and be sure to make it a Feature Service. Go to the new shapefile feature service details page and enable editing. Open a new map, add your shapefile feature service, choose a map background then save the map. On your Android device, open the Collector App and log into your ArcGIS Online account and find your new map. Edit your points.