Two-factor Authentication closed loop. Devices can't approve each other! After recently updating iOS on my iPhone I was asked to approve my iPhone from another Apple device of mine. I believe an approval code was sent that I never received because it was sent to the device I am trying to approve. I saw my phone number appear on the screen, and confirmed it because it is my current number, not realizing where this would lead.

I can't approve my iPhone from my Mac because it's not running El Capitan yet. I have now started a lengthy Time Machine backup and am looking into the steps for a clean install since the Mac has performance issues that a standard update will likely not solve. This had to be done anyway, but it's going to be a process, and I still don't know if my iPhone will trust my Mac since the Mac doesn't have an existing history of 2FA usage.

I can't approve my iPhone from the household iPad because it uses another family member's account for iCloud. I hoped that because I make iTunes purchases on the iPad with my Apple ID that the iPhone would trust it, but it does not. In fact, the opposite has happened - after signing in with a now-suspect Apple ID the iPad is now also waiting for approval and refusing to trust the iPhone.

I cannot log into icloud.com for the same reason, so there's no hope of authenticating from there.

This has become a nightmare spiraling out of control, with my Apple devices all asking to be approved and none of them trusting each other. What can I do to prove that I am me, and get my iCloud and devices functioning again?
If you select your phone number, your phone will receive the text and automatically fill in the code for you. I do not believe that macs are able to receive 2FA codes.