One of Gmail's goals is to reduce what it thinks are unnecessary emails that might be routed to you inbox, part of this entails not routing messages that you send to your own alias to your inbox. This setting is explained in the link below.
The steps below will explain how to go about changing your settings so that you can send to your own address and have it arrive in your inbox.
1. In Gmail go to the gear icon and click on Settings.
2. Click on the Accounts tab along the top.
3. Next to Send Mail as: you will see the email addresses associated with your account. Find the address you would like to send to have show up in your inbox. In the case below it will be the firstname.lastname@example.org account that will be changed so that it can be sent to and show up in the inbox, note that "Not an alias" denotation under the address, this is the setting that will be changed. Click on "edit info" next to the desired address.
4.In the pop up window that is created check the box next to "Treat as an alias" and then click "Save Changes"
5. You should now be able to send a test email to the address that you just made the changes to and it should arrive in your inbox.