Q: I can receive texts but can't send them?

Did you already check for carrier updates?

iOS: Updating your carrier settings - Apple Support

Did you check this article as well?

If you can't send or receive messages on your iPhone, iPad, or iPod touch

Can you send and receive iMessages?

If yes, did you make sure that "send as SMS if iMessage is not available" is selected in Settings/Messages?

Your phone number is selected in "Send and receive at" and there is no mail address selected?

Did you already reset the network settings in Settings/General/Reset/Network settings?

Messaging is active from the carrier side for your SIM card?

This would be the last step before setting it up as new device without using any backup data, only adding the personal info manually and checking the message functions again.

Use iTunes to restore your iOS device to factory settings - Apple Support