Hey there! The great thing is, that's exactly why the pick guard is there! Keep focusing on proper strumming technique. You're doing all the right stuff!

Check out these lessons on strumming, they should provide some more insight:

https://www.guitartricks.com/search.php?search=strumming

As far as moving on to another song, you should move on when you feel comforatble. You don't have to have it down perfectly. And you can always come back to a particular song!