You make contradictory statements. Either you purchased it without an account or you purchased it while being logged into an account.
But this does not matter. If you did not receive an email after your purchase, something is wrong.
Either a typo in the mail adress or it is stuck in the mail queue or something like that. A mail can be on it's way for several days. That is unusual, but not all mails are delievered instantly. But the usual issue is, that the received mail got sortet into your spam folder. That depends on your mail client. You might have more than one layer of spam folders. One in your client, one on your internet service provider and so on.
The extreme case is, that the Itch server cannot send you mails at all. Since you have an account, I doubt that, since you received a verify your mail adress mail and verified your mail adress of the account.
If you have a transaction on Paypal with Itch being the receipient, use your Paypal mail adress on https://itch.io/docs/buying/already-bought to resend you the associated download keys.