I think I figured it out: Go to Settings>Apps>Application Manager>Dictionary>Storage
Press the "Clear Data" and "Clear Cache" buttons
Now go to Settings>Language and Input>Default Keyboard and select the keyboard you want to use (Swype, etc)
Emojis are back!
Also just for good measure I followed JohnMcL7's advice:
Apps>Settings>Language and Input>Virtual Keyboard>Samsung Keyboard>About Samsung Keyboard (at bottom)>press update button (downloads and installs an update)
Press the "Clear Data" and "Clear Cache" buttons
Now go to Settings>Language and Input>Default Keyboard and select the keyboard you want to use (Swype, etc)
Emojis are back!
Also just for good measure I followed JohnMcL7's advice:
Apps>Settings>Language and Input>Virtual Keyboard>Samsung Keyboard>About Samsung Keyboard (at bottom)>press update button (downloads and installs an update)