Why so desperate to get the message immediately and yet "I’ll just send a message in a day or two if I don’t hear back.".
Having said that, I know the feeling. Your phone was in airplane mode for a while and now all those sexy messages, job offers, lottery win notifications etc, didn't get through.
Reboot your phone if you like - it won't make any difference. Don't take the sim card out, that's a total waste of time. Just wait. If it was an iMessage you'd've got it by now. If it was a normal text (some people have the settings such that if an imessage fails it reverts to sms) then you're dependent on your network retrying. That can sometimes take up to 15 minutes.
Oh, and if you reboot your phone, that's exactly when the person will send a message saying "Why didn't you reply????"