1. From the practical point of view, the difference will not have any problem. As for example, in Government service, people generally retire on the last day of the month in which they are born. So, if you join Government service, you will retire on 30th April, 2051 (irrespective of your date of birth being recorded as 14th April or 15th April). In private sector also, the same rule is in vogue.
2. All Government documents including your birth certificate indicate your date of birth as 15th April, 1991. Then how do you establish your claim that your actual date of birth is 14th April, 1991?
3. I think you have passed your Xth Standard examination in 2007 and XIIth Standard examination in 2009. It is very difficult to change the date of birth in the documents after such a long time, especially when you don't have any supporting document.
So, I think it would be better for you to ignore this small discrepancy, which in any case can't be pointed out at any stage.
Come on, have a fight. Don't shoot and scoot.