Hi, i feel bad to here your story, cause i had experienced similar issue with CheapOair. When i was booking, it clearly said beside the "Booking" button that Its fully refundable within 30mins after booking(or some time i can't remember).
After I found that I booked on the wrong date, definitely within 10 mins of booking, I called them, they said their tickets are all non refundable........
Finally, I emailed to them with complain and they refund the ticket with some charge. You could try to email them. Cause the call centre are useless.
Another thing is that, they may even not issue the ticket when you ask for refund. Sometimes, they sell you tickets, get your money, and issue a "confirmation code" first, when the airlines open cheaper tickets for sale, they will but those cheaper ticket for you and then issue it.