How to Not Be A Grammar Nazi

I have a grammar problem. For some reason, I can't figure out the two pronouns "I" and "me." My mom even made me write a report on it, and I still mix them up. When my brother and I want to go outside, I tell my mom that, "me and Travis," are going outside. When my mom and I sit down to watch a show, "Mom and me" are watching it. There's another problem that I have along with it, though: I'm very quick to point out other people's grammatical errors. That reminds me of a Bible verse . . .
"Why do you see the speck that is in your brother’s eye, but do not notice the log that is in your own eye? 4Or how can you say to your brother, 'Let me take the speck out of your eye,' when there is the log in your own eye? 5You hypocrite, first take the log out of your own eye, and then you will see clearly to take the speck out of your brother’s eye." -Matthew 7:3-5
For me, it's really easy to catch my mom or my dad or a friend saying "me" instead of "I" or "I" instead of "me." When I jump in at the first opportunity to quickly point out their error, according to Jesus, I'm being a hypocrite. What's a hypocrite, you ask? Well, it's . . . "a person who pretends to have virtues, moral or religious beliefs, principles, etc., that he or she does not actually possess, esp. a person whose actions believe stated beliefs." It's not good to be a hypocrite.
Do you remember the Pharisees back in Jesus' day? The ones who, when giving their offering, would use lots of big coins and clank them loudly, so everyone would see how "righteous" they were? And the ones who, when fasting, looked sad and moaned and groaned loudly, so that everyone knew that they were fasting? Jesus called them hypocrites (Matt. 23:13, Matt. 23:15, Matt. 23:23, Matt. 23:25, Matt. 23:27, Matt. 23:29). He didn't exactly see fit to tell them just one or two times, though. 6 times in just one chapter! Hypocrisy is serious. Jesus seeing fit to point out the sin of hypocrisy 6 times in just one chapter proves to us how important it is.
Don't get down, though. There is a cure for hypocrisy: Fix your problem first, then gently correct others (only when needed), keeping in mind that you used to have that problem. The lesson that I learned: DON'T BE A GRAMMAR NAZI!