eat fast food or takeout. I could easily eat double cheeseburgers for every meal.

That's how it has to be: you have the authority to apologize to someone, but they have no obligation to accept. Perception is reality, and even if you know you did nothing wrong, you must respect a person's reaction to your apology. You responded correctly, and it's a valuable lesson for the future. When we make a mistake, we often have no choice but to apologize. After that, you just have to keep going, confident that you've done everything you can.