Do you think I should say sorry?
Really? What makes you want to apologize?
Because it's the polite thing to do
If you feel like you have done something wrong, then you should apologize.  Even if a long time has passed, it is never too late.
It's only for my mom, I want her to lighten up and stop being mad at me.
That's fine, and actually a very good reason. It's never too late to apologize to someone you care for.