I guess I'll first note that I don't have a Masters degree so I can't really comment from that perspective of things. There are a few things that I do think I could share that might be useful though.
I found myself in a similar situation to your intial one, in that I went to school for computer programming but found I really wanted to be in web development. There are a few factors that will really depend on your location and situation though such as what jobs are available to you and which of those suit your current conditions. The great thing about this field is that with the right skill sets it is generally easier to find work (compared to job market as a whole). So to an extent it's entirely possible that you could be better off not investing in something as grand as that Masters degree. It's still possible to educate yourself on industry standards and new changes such as those that come with HTML5 and CSS3.
But having said all of that, if you do have the time, money and drive to push yourself to get a Masters in Web Design/Development then it can still pay off for you in the end. Obviously, any degree is an investment and another great thing about this field is that with being skilled and technical as a job, you can expect great pay rates/salaries, so the investment would pay for itself in time and you could of course secure a very solid financial future.
In the end, this really comes down to where you want to take your career from this point. You say you have been working in the field or a few years now so it seems you are more or less wondering if you should further your education to in turn further your career in this field. But personally, if you're already doing what you love it would seem that you don't need to go out and push for the extra degree. You can still further your knowledge while building up your experience in this field.
And also, in regard to the decision between Web Development or Graphic Design, you'd be better off going with Web Development in the end. It's true there are changes over time making things that were important a few years ago obsolete, however Web Development covers an array of languages and techniques and most of them tend to stay pretty similar. HTML5 and CSS3 have pushed us in to a new age of web development, but core principles and concepts remain the same across the industry.