How can I ensure about my R^2 score?
$ R^2 $ shows what variation of your purpose variable is described by independent variables. So their synergetic effect could give you good better answer than their correlation. Better use $ R^2 adjusted $. Look at p-values of your variables and think about their real correlation. Are they important in real life. If they have any adequate relationship, so your regression is right.

Hope it will help.