LBF Travel Charged for a flight LBF didn't pay for San Diego California

0n 6/21/17 my family needed airfair to Mexioco for a family trip.  Our previous arrangements were not working out.  we found LBF Travel on the internet and booked.  We got to the airport and checked in at the kiosk with our pass ports which cleared but we could  not get our boarding passes.  We went to the front desk and while the clerk informed us that our name was in the system, the tickets had not been paid for (we paid for the tickets with our cc on ine).  The front desk clerk kept checking for payment and it still had not appeared.  about an hour befor the flight was to take off, the clerk advised us to purchase the tickets from American Airlines and we also had to pay a $45.00 Penalty for each ticket for purchasing them at the front desk. I have been going back and forth with this dispute.  LBF Travel has not shown any proof that their tickets were used, but I have given proof of the tickets I purchased from The American Airlines Counter.  My Next stop is the BBB to report these crooks!!!