Do my text messages get deleted if I restore my phone?

Text messages are saved on an iPhone backup.

So if you restore a backup, you will have the text messages that were present when the backup was created.

Restore to factory settings would remove text messages, as well as other content.

So one of two situations apply:

1. It would be just fine to dispose of the text messages. Saving text messages is like saving recording of old voice conversations; they quickly become obsolete. I'll restore the iPhone.
2. I really need those text messages. So I'll restore and use a backup to recapture them. Restore your iPhone, iPad, or iPod touch from a backup - Apple Support