While it sucks that your supervisor is so out of touch with your position, being victimized by that is partially on you if you allow it. Whether or not you can get the reprimand out of your record won’t be entirely up to you, but taking steps to prevent recurrence will be. Make it clear to your supervisor, HR, and the VP if possible, that you are deserving of more respect than has been demonstrated, and that you won’t have this. Assert yourself as the expert in your field and act, if necessary, as though they’d be dead in the water without you. Express your unemotional and unrelenting resolve to produce the best possible design product for the company no matter how many revisions it takes, and tell them straight out that quibbling over how many changes are too many is not only a waste of their executive time, but just as surely, beneath you.
You may not feel as though you’re in a position to be that assertive, but I’ve found that nearly always, people who push others around stop when someone pushes back. Others’ confidence in you must start with your own confidence in yourself. Years ago, I had some talks with a “career coach” that were largely about how to write a good resume and cover letter (and that stuff changes all the time), but at some point he threw in this: “Always be respectful…and act like you own the place.” Later he rephrased: “Don’t be arrogant, but leave no doubt that your role is crucial, and you own it.” Best advice I ever got, and it has been critical to survival in my current position.