From what you've told us already we can probably assume the follwing is true:
1. Since you said you received a confirmation email or welcome email from public, it must mean that Public has your correct email address already, so whateven email account you recieved their emails is the one they have on file.
2. Since you say your phone is working and you can receive calls etc, it must mean that your public mobile service is working, so check your sim card and your phone left hand top corner to confirm that it says Public Mobile on phone screen top left corner - if it says that then it means your sim card is activated onto Public Mobile system.
3. Since you say you can't create a self-serve account because it says the email is invalid and the phone number is invalid or already used, it probably means that either you are entering the wrong password or that your email is too long or something that the system has your email correct but for some reason when you try to use it for creating or logging in to self-serve it's not being accepted. This happened to me that my email was fine for creating my account but too long to be used in the self-serve page. In this case you'll have to contact the Moderator Team via private message to fix things.
The fact that your phone is connected to Public and that you're getting emails from Public seems to indicate that Public has all your info correctly, but the problem is that you are entering that info incorrectly - like either the problem is you have the caps lock button on or something when you are putting in your password or email, or the problem is from Public like what happened to me etc your email is fine for activation but too long or not fine for the self-serve page for some reason.
