I've just completed my bachelor's degree in Mechanical engineering. I worked as web developer for a bit, that's when I came across game design. I had every intention of pursuing a master's degree in game design, thinking that a game school can help me build my portfolio much better as compared to me doing it on my own. Also, game school will help be build contacts in the industry. But upon reading many online forums, I've realized many game designers themselves suggest that a formal education is not helpful. The master's program is 2 years long and I do not want to waste time and money if it isn't really helpful. Any advice on whether I should do a formal course or wing it on my own?

Education is specific to your region of the world.  Generally a master's degree is one you should pursue if you want the education rather than for credentials.

You write about game design, but do you actually mean design?  Game designers generally don't write game code, and don't make game artwork. Game Designer is also a senior-level role that usually comes up through other disciplines; there are rarely some positions like level designer that can lead to a game designer role, but the positions are extremely rare. Many schools offer a program of study which they call game design, but is actually an introduction to a mix of disciplines like programming, animation, art, and sound. 

The actual job of game design doesn't tend to fit well into a single degree because it relies on so many different backgrounds. Biggest of all is communications since that is the core of the job, but building gameplay designs requires a mix of psychology, mathematics including some statistics, numbers and numeric game theory, art theory, music theory, history, storytelling, plus you need to understand business management and communications, and other skills unique to each game depending on the nature of the game. Game design also relies on experience of having studied other games and determining what makes them fun, or what makes them non-fun.   

Ironically, because there are so few entry level jobs for game designers (it is a senior level position, few designers are needed relative to other roles, and designers are generally pulled from other roles) the schools that do teach actual game design tend to be poor choices for getting the job since most people will enter through other disciplines. In many ways you are more likely to get a game design job by following education that isn't for game design.

All of that aside, for a master's program if you want the degree for your own education and you've got the funds and ability to get the degree, then go for it. If you're doing it because you think it will give you the job title, probably don't.