assuming I've understood you correctly, you have a geodatabase with a number of point feature classes, and you want to pass each feature class once through your model. If this is the case, you should use the iterate feature classes tool.
If all your points are in the same feature class, you should use the Iterate Field Value tool instead. With this tool, you can group by a certain field, (if you have multiple points that need to go through together) or just group by ObjectID (or another unique identifier field) if you want each point to go through on its own.
I hope this helps!