A bit more information would help...
Do you mean on your phone or tablet?
What happens if you use the webmail portal for gmail?
What happens when you send an email from the web portal to yourself?
What happens when you send an email from the web portal to someone else?
How many other accounts have you sent test mails from to your gmail account?
And were there any error messages?
Are you using the standard xxxx@gmail.com format or a personal domain?