The total number of Snaps is displayed under the SnapCode and it's available on your profile. You can check this information on the official Snapchat blog. Access the page and you will see where to look for the total number of snaps.
On Android, the highscore represents the total number of snaps you have sent and received. There is no possibility to see the ones you have just sent, only a total of it.
More info on the support page: https://support.snapchat.com/a/hiscore