Most likely, you are looking in the wrong chat. The access codes come to a chat called “Telegram”. News about updates also is there.

Often the code will not come if the account has a cloud password (2FA) enabled. Deactivate the cloud password and request the code again. Once the activation is complete, the cloud password can be re-enabled.

If you are sure, that the phone number is correct, but nothing works, it means the code has been requested too many times. You need to wait, sometimes for up to 24 hours. Keep calm, make sure your cloud password is disabled and try requesting a new code every few hours (but not more often).