@Anderson555: Is the issue affecting all contacts, or just certain ones? If you open the Messages app and tap on a relevant conversation/message, can you see a time to the bottom left of the message to indicated that it has sent successfully?
While the Messages app is open, tap the 3 dots in the top right > Settings > More Settings > Text Messages > Show When Delivered > On > Back > Multimedia Messages > Show When Delivered > On > Show When Read > On. With these options enabled, you will be able to keep track of the status of the message once it has been sent. I also recommend enabling Mobile Data, just in case the messages contain any images/emojis, or they exceed the character limit as determined by your mobile network.