Hank here from Shopify.
Editing of the SMS templates is not available on the trial or on plans that have not yet made a payment, but you mentioned that you have paid an invoice, so this option should be available to you within the admin.
As this is account specific, I will just need to verify your account. I will send you an email to the email address attached to this forum's account and confirm some security questions about your store. Once you reply to that email, I will look into this further for you.