Hi Michele,
Thanks for this suggestion. At present self-referrals like this are intentionally blocked to prevent abuse of the affiliate system.
But never fear, the user system was designed with such web designers in mind; they can create individual Client Accounts for each client and then send an invite to login and submit payment. Or the client can signup directly using an affiliate link and then invite the designer to be an additional user on the account.
Check out some details here: https://docs.whmcs.com/Users_and_Accounts