You may be experiencing any of these issues:
Many SMS issues are network-related. Contact your carrier for advice on possible network issues.
In rare circumstances, SMS messages can become stuck in a pending state and are unable to be sent. This can be resolved by a system update. Ensure the device software is fully updated, by following these steps:
Third-party messaging apps may also cause multiple duplicate SMS messages to be received. Clearing the data cache may resolve the issue. See How to wipe your cache partition.
A factory data reset can resolve some send and receive issues. See How to factory reset a device.