Best of luck with your internship and one-year master programm. I think this is a great first-step in terms of showing your profile has changed since before, not to mention doing this for the value it will bring you personally.
At the end of the day, as people have mentioned here before, what will really matter and what firms really care about is how your profile has changed since you've last interviewed, However, I think it is extremely valuable and wortwhile to network as well to present your point of view and your story with some peope at the firm to ensure that they are fully aware of how your profile has changed. A lot of times application reviewers might see your resume but not necessarily understand or clearly see what has changed, and this is way some networking and phone calls may help,
Just very recently, a friend of mine was interviewing with MBB and had previously interviewed with both about a year ago. While he did a lot in between (worked with a startup and a smaller consulting firm), I advised him to also go out of his way and network with some individuals inside both companies to ensure that these changes are visible and well-understood to those reviewing his application.
I hope this helps and do let me know if there is anything else I can do.
Wishing you the best of luck,