Not receiving SMS messages on iPhone

I get a notice (from Google, let's say) that a confirmation code will be sent (by text message) to my cell phone number (which happens to be an iPhone).

I look for the confirmation code in the green balloon message stash, but I find nothing there. This has been a recurring problem. The original seemingly simple transaction blows up into several hours of futile tail-chasing.

Then, I tried to log into an Apple Community forum to find out what was going on. The forum wanted my Apple ID. I have not used it for a long time and I do not know it now. My best guesses failed. I tried to find my Apple ID and reset my password, and I think I reset my password, but I could not find my Apple ID. Apparently it is an email address, but it is not the one I was using as I tried and failed to find my Apple ID.

I wouldn't care much about not finding the Apple ID except I needed it to get advice on an Apple troubleshooting forum...re the SMS message problem noted above.

It may be that I am missing something basic and the solution is simple. Right now, though, it seems infernally complicated. What to do?