My iPhone 4 does not receive confirmation code sms messages

Many times, when, for instance, I am recovering a password, or signing up for some sort of online service, the company, or website, wihen all the forms are complete and the final enter button pushed, shows a screen saying "a verification code will be sent to your mobile phone using this number ( shows my cell number)", but no text message ever arrives. I can sometimes work around it by havin the code sent as an email, or phone call, but some organizations, for instance Way2Ride NY, don't offer that option. It happens globally, across nearly all websites. Doesn't matter how long I wait, or how many times I try thr "tap to resend" button! I never get a text. I have the Google 2 step verification app, and when a site asks for a code from that, it works fine, but it seems that when a random number is generated by a site, any site, and sent by text to my iPhone, it never comes through. Have I accidentally enabl d some filter or something?