I would tell everyone if I was immortal

Avoiding torture is why you would hide it. There would be two kinds of people in the world for you. Those you want what you have, and those who hate what you are. The ones who want your immortality would hunt you to experiment on your body and torture the means of how you became immortal out of you. There are hundreds of rich and powerful people who would want immortality and would kidnap you in a second and secret you away somewhere to get it. The second kind are the ones that would believe you are an abomination to god and/or nature and would seek to kill you for their extremist reasons.

The world is a hateful, jealous place. Look at how people treat celebrities for their fame and money, and now imagine that you have something far more valuable and desired than that.