@Speedbuggy: Please can you confirm the model number and current Android version of the device you're accessing your emails on? Are you using the stock Samsung Email application? If you sign in to your email account via an internet browser, are you still able to send emails as you would normally?
@devonblue: If you open the Samsung Email app > Tap the 3 lines in the top left > All Folders, you should find your outbox here. If not, tap the cog symbol in the top right of the pop up window > Manage Folders, and you should be able to select it from here.