I know English uses a definite article with the names of government institutions (eg: the White House, the State Capitol and the Pentagon, etc.). But I don't know if it's the same case with the names of schools, colleges and universities that are run by a particular local government. The college I go to is also a government institution and it's name is "Government Polytechnic". Would it be grammatical, if I used a definite article before my college name? (Note: There is one such college in each district of my state.)
Probably not, although as it is a proper name, any institution can call itself whatever it likes to.
In the U.S., most colleges do not use the article, such as Columbia University, Harvard University, etc. However, what most people call Ohio State makes a point of letting anyone who will listen that they are The Ohio State University (even though their normal initialism is OSU, not TOSU. As per Wikipedia--The Ohio State University, commonly referred to as Ohio State or OSU, is a public research university in Columbus, Ohio.
However, when the word College, University or the like comes first, most people will insert the article in everyday speech: I went to the College of New Rochelle. Wikipedia says--The University of Kentucky (UK) is a public co-educational university in Lexington, Kentucky. (Note the lack of bolding on "the".)
Other exceptions do exist: Wikipedia states--The Cooper Union for the Advancement of Science and Art, commonly referred to simply as Cooper Union, is a privately funded college located in Cooper Square in the East Village neighborhood of Manhattan, New York City.