We're fine, thanks.
The fact is thate are no planetary effects from this 'close' Mars approach. The mass of Mars has an insignificant effect at this distance. It's still over 100 times further away than the moon. The effect of gravity decreases as the square of the distance. Lets assume that the moon and Mars have roughly the same mass (Mars is actually 10x heavier) so at 100x further it's 100x100 = 10,000 times less effect than the moon.
Gravity truth be told is a weak force.
Fot thoseyoung enough to still be in school, a high school physics course is a great way to learn all about this stuff and satisfy your healthy curiosity.

-p