Is my pistol case okay for for flying on a plane?

I plan on flying with my firearm for the first time. I will be putting it in a lockable hard case and checking it in my luggage. I am going from Connecticut to Utah. I will be flying American Airlines going, and United Airlines coming back. I checked the TSA website as well as the websites for both the airlines to get specific requirements. I was thinking of putting it in the hard case that came with my Kahr. I heard that some airports have rejected certain hard cases, though. I don't know if I should buy another one or stick with the one I have. I'm kind of poor and don't want to spend the money if I don't have to. I called AA and asked what the requirements for the case were, but the person I talked to sounded like she had no clue and was just reading off of A COMPUTER screen. Here are pictures of it. Please look at the pictures and tell me what you think. Also, any other advise or personal experience you have from flying with a firearm is greatly appreciated.