There could be several reasons for that but I would expect that it comes down to permissions. In order to create projects you need to be a member of the JIRA Administrators group. This a global permission level. You can find out more about different levels of global permissions here.
If you do not have the icon "cog" you are not logged in as an administrator. By definition you will see the cog if you are an admin. Without the "cog" you cannot perform any administrative functions. Someone must have those credentials in your organization. They will have to go to the User Management | Global Permissions section and add you as a user to the JIRA addministrators (or JIRA System Administrator) group. See attached screen shot.
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