Hi KarenOC,
Before moving on, I would like to confirm more information.
1) As for "I cannot get my own domain e-mail", do you mean you can't receive the email from other users?
2) Are you using Microsoft Office 365 for enterprises or Microsoft Office 365 for professionals and small businesses?
If you are using Microsoft Office 365 for enterprises, have you added DNS records to configure your domain for Exchange Online?
You can refer to this link: onlinehelp.microsoft.com/.../jj655360.aspx
If you are using Microsoft Office 365 for professionals and small businesses, have you changed the domain’s name server (NS) records on your domain registrar to the Office 365 primary and secondary name servers?
You can refer to this link: onlinehelp.microsoft.com/.../gg549203.aspx
Thanks,
Jerry Cen