The first thing to do is to check the message centre number is correct. You should be able to get this from your carrier’s website.
If it is then turn the phone off, leave for a few minutes. Turn it on. Wait a few minutes.
Send a fresh message to the one of the people you’ve been having problems with. Do not reply to one of their messages, it MUST be a fresh message (it’s technical but I’ll explain if you want.)
If that shows the error then call or contact your carrier explaining that text messages are taking too long to send and arriving late.