You've only committed assault if you cause psychological distress to the victim where they believe they are going to be physically harmed by your action.
Let's have some examples:
If you wind up to punch someone and then stop an inch away from their face without hitting them you have committed only assault.
If you wind up to punch someone and then punch them in the face you have committed assault and battery.
If you punch someone in the back of the head you have committed only battery because they did not see it coming.
If you wind up to punch someone in the back of the head and stop an inch away you have done nothing.
As for your hug it could be interpreted from her point of view if she stretched it that it was assault but really I wouldn't worry.
