So you set your Time Machine to backup your Mac to an external hard drive. If the Mac has formatted the drive then it is too late. Right click > Get Info on the ext drive in Finder and see what it's formatted to. If it is not formatted then it should say something like MS-DOS (FAT32) if it was formatted for Time Machine then I believe it would say MacOS Journaled
If you already see a backup of the Mac such as "Bob's iMac" then it has already created a backup to the external.
I don't mean to be rude by saying this, just giving some advice to you (because I have lost photos before), this is why you always keep 3 copies of everything! Two with you and one "in the cloud" such as Google Photos or Flickr.