I don't know if you're too sensitive to what people say (or what you think they say); only you can answer that question. If you sense it may be true, ask God to help you become less concerned about yourself - and more concerned about others.
But I do know this: Gossiping can be one of the most destructive and cruelest habits any person can practice. It destroys the reputation of others because it's often based on half-truths or outright lies. It also destroys the character of the person who gossips; who is going to trust you as a friend if you have a reputation as a gossip? No wonder the Bible says, "A perverse man stirs up dissension, and a gossip separates close friends" (Proverbs 16:28).
Have you ever asked yourself why some people gossip? Often a person gossips simply because they want to appear important or "in the know." But that's a very self-centered motive - and not one that God will honor. Sometimes, however, people gossip from very evil motives, deliberately trying to tear down others. Needless to say, this is wrong in God's eyes.
Commit your tongue - and your whole life - to Jesus Christ. Then make it your goal always to speak truthfully, and with words that heal. The Bible says, "Do not let any unwholesome talk come out of your mouths, but only what is helpful for building others up" (Ephesians 4:29).