I have been really convicted for about a decade not to gossip, and have been working on that ever since. I actively hate gossip, but I still do it when I get frustrated. But I think it's one of the great scourges of mankind.
Then last spring, I got really convicted not to worry. That's one of the other great scourges of mankind.
The Biblical mandates not to worry (see, for example, the end of Matthew 6, Luke 12:22-26, Philippians 4:6-7, 1 Peter 5:6-7, and Hebrews 13:6) and not to gossip (see Ephesians 4:29, Proverbs 16:28, Proverbs 20:19, and James 1:26, among others) are really clear. There aren't any gray areas. God says, "don't."
I am encouraged by my friends who have also decided to opt out of the gossip-and-worry circuit. It is hard work. And I will give it to you straight...it can be a little lonely sometimes, because dispensing with gossip and worry is really counter-cultural. You will start noticing that gossip and worry are foundational to a lot of conversations that you have to just walk away from or even actively disagree with. And I have found it's not enough just to have thick skin, or a stubborn determination -- I need the full armor of God on (see Ephesians 6:16,17).
Replacing worry and gossip with prayer is key.
My friend Bianca recommended this book, and it has been really helpful in reducing my anxiety. I will battle the urge to worry my whole life, but it's a good and worth-it battle. :)