Someone is most likely spoofing your number and making it appear as though you sent it. It’s frightening how easy it is to do. There have even been cases where people have hacked into a person’s account even with 2FA enabled because they receive the authorization code as though it was you.
Cellular providers are trying to come up with a more secure messaging system to replace SMS. iMessage is more secure. One way they could tell if it was really you would be if they also use iMessage as it uses end-to-end encryption’s and if they receive a message from you it would be blue and not green.