do the prisons approve me or the actual phone number for inmate calls?

The approval process is based on the actual person, not a phone number. Approved people are allowed to change their number at any time for any reason. If this occurs, the facility staff does not have to relay the new number to the inmate. They might, but the rules are against staff passing notes from the outside. You know inmateAID has two services to do just that. Please let us know if you need further help.