Appointment Times conflict with...themselves?

My schedule is clear, a client books an appointment and it says there is a time conflict. When I look at the time conflict for that appointment, it lists that new appointment as the time conflict with itself.  The clients do not receive any notifications that they ever booked that appointment even though they booked it themselves in one of my available time slots.  The workflows are set up, the notifications are turned on, their emails are correct, it doesn’t go to their spam folders. I have a feeling it all comes back to that weird time conflict the appointment has with itself. Please Help. No one has figured it out yet.