Should I Be Worry or Worried?

Both of your sentences are correct, and they mean pretty much the same thing. But if you want to talk about a general, long-lasting worry, say I worry about you, and if you want to talk about a specific worry related to a specific event that's happening now (or happened recently), you can say I'm worried about you.

Is it worry or worried?

Worry is the verb, worried is the adjective. If you worry, you are worried, and if you are worried, you are worrying.

Should be worried meaning?

said about or to someone who clearly has no need to worry: She should worry! She hasn't a problem in the world.