Generally, to create a project, and if you are under an Organization, you need an
"roles/resourcemanager.projectCreator". Hence, you may contact the Organization admin and ask them to assign the role/permissions.
As for the second question about "No Organization", if your account is associated to an Organization (domain) you cannot create Projects outside of it. That is, if there is an Organization node associated with your domain, then all Projects and billing accounts that you create will be associated with that Organization. More about the benefit is explained in this
document.
If you would like to create a project outside the organization, you would have to use a different account (such as gmail) and most probably a create or use a different billing account if your non-domain Google account does not have
Billing IAM roles (such as Billing user) on the Organization Billing account.
I hope this clarifies it for you.