It all depends on how you send messages because TextMe supports sending real SMS messages delivered as a normal SMS message and messages between users that can be sent through Internet. For this type of messages, there should be a simple sign to indicate if the messages was sent or not. Normal SMS messages are delivered by the carrier network and you can't really know when they're delivered or not unless the other user responds.
The description on the Play Store and App Store is hard to understand and no other indication is provided.
