If you are just using the Companies House Public Data API you do not need OAuth (and I don’t think it works with the data api, documents api or streaming API - I think it is only used for e.g. the Filing API e.g. if you want to make a filing / update company information).
When you registered did you choose the “live” system?
Have you registered your server IP with Companies House, OR used the workaround for “localhost” use, OR registered a javascript url (I’m not sure which you’d need for your Postman use)?
If not certain about any of these see the following threads (and also the localhost one above):
https://forum.aws.chdev.org/t/postman-api-call/3740/8
https://forum.aws.chdev.org/t/invalid-authorization-error-in-api/3599/9
Good luck