I checked up on my taxes and it said that they went through to a direct deposit but I do not have a bank account

Once the Where's My Refund? site shows "Refund Sent" and a date, it could take up to 5 days for it to be reflected in your bank account, it all depends on the bank, how and when funds are credited. If you used the Refund Processing Service (option for paying your TurboTax fee by deducting it from your federal tax refund), this can add a couple more days also.