I do not have Write permission. Is there a way I can still create records?

Yes, with the help of Vtiger's Workflows. Workflows can create/update records in the CRM account owner's name, even if record owners do not have Write permission. This is called the account owner context.

Example: Consider a workflow that is configured to create a deal record when Lead Status = Hot.
Let us say, a sales rep who does not have Write permission for Deals edits a lead record and sets Lead Status = Hot. As a result, a deal record gets created with the Created By and Last Modified By fields having the CRM account owner's name.

To learn more about workflows, click here.