Large Dog shipping / traveling

We flew from Miami to STX in Dec with our dog in a large crate not xlarge and flew from STX to Ca in March and had no problems the vet said I could give her Benadryl to help her nerves but not knock her out!! She is a big breed dog and with her kennel coming back it was over weight but still no problems and that was American Airlines but due to how long of a flight and how nervous my dog is at loud noises I would NEVER put her through that again, she see's a suitcase now and is so freaked out!! I recommend reading the airlines website and if I had a question I called and asked just to be safe! Good Luck