Would my computer and my files be safe from an hacker if I have Norton Internet security on ?

I got someone mad and it was a forum adminstrator or moderator from a forum website who is mad at me and I believe he is after me or something. He's also the website owner I think. He has claim that he knows who I am because I think he traced my ip address or something. He has given me threats that he will forward all that he knows about me to government authorities in the U.S and in Vietnam. I've talked to a computer expert and he says that tracing an ip address only gives you the city and state and the ISP provider and he says this guy is trying to scare me. The computer expert also says that because I have Norton Internet Security turned on and up to date that my computer should be fine. I'm just trying to take measures to protect myself. Would my computer and my computer files be safe from an hacking attempt if I have Norton Internet Security ? Can you please help me out ?? I'm extremely paranoided. I'm not going back to that website but I want to know if I am safe from someone finding out who I am.