Plumbing! I needed to fix my bathroom faucet, so I turned hot and cold water faucets off under the sink.?

Now, when I turned them on, they are dripping. My plumbing was installed 2 years ago and everything is pretty new. The nipple which holds the faucet handle is impossible to turn in any direction and water is dripping from it. How can I tighten is?Would it work if I just put silicon around it to stop water? I know that's the best is to call plumber, but they charge so much even for little things. Please ,advise.