“So, Are you Immortal now?
Well, No this doesn't make you immortal because even if you suicide you will of eventually die by aging or accident or any disease.”

Aren’t you confusing here bodily immortality and consciousness immortality? Because in the example above you say that “everytime you Pulles the trigger the timeline splits into two sub timeline.” Who is to say that when the timeline for your body ends, the timeline for your consciousness also ends?

So giving this thought experiment, you cannot simply come to that conclusion that, “no, this doesn’t make you immortal”, because that’s just relative.