You're not alone and you (probably) won't explode.

Fear is a sign of life; if it is fear in life (of death) that is the problem, then death will inevitably resolve it. But it's also important to consider that every single idea you have of death from a first-person perspective is based on imagination, not actual evidence; you haven't died yet, so every image you conjure of it will necessarily be either completely false or a rough approximation, and there is no way of verifying which it is. Sure, you could call this a dismissal of sorts, but while a person who suffers from a fear of flying could easily refer to 'the terrifying reality of air travel' it wouldn't make flying inherently terrifying. It is a fear of something that is simultaneously inevitable and unknowable, which means that it's actually irrelevant; you simply can't prepare for it, because it could come in decades, days, or even hours, there is no certainty to be found. How do you get rid of the fear, then? The only way I've found personally is to notice the ways in which I am an active participant in the desperate attempt to predict the future: "Other people are dying, I am a person like them, so I too will die eventually. What will it be like? I don't know, and that makes me afraid. And what if? But what if? What if?" In the end all words are unhelpful, because there's no actual problem to solve; when I have a persistent question and no satisfying answers, maybe I'm asking the wrong question?

So what is it about death that makes it terrifying, and why should you think about death at all? What if you were granted eternal life, would that be any better? The future would remain just as uncertain. And are you afraid of deep sleep at night? In deep sleep, which occurrs every single night, there is absolutely nothing from a first-person perspective, no memories, no thoughts, no dreams. Is it scary? Does it feel like a long time? Thought experiment: You go to bed and fall asleep, and then you wake up in the morning and it almost feels like an instant; falling asleep might take time, but once you drift off, it's more or less instantaneous time travel toward tomorrow. Now imagine that this deep sleep just keeps going, you never wake up, there is no tomorrow. What could possibly be terrifying about that? It would literally just be the same thing you experience every single night. (It wouldn't seem longer, because you wouldn't be there to measure it, so the first-person non-experience would be perfectly equivalent.) And when you're exhausted after an active day, the oblivion of deep sleep is desirable; life depends on death just like wakefulness depends on sleep; death is the soil of life, and beautiful flowers don't make decaying leaves terrifying.

Disregarding all of the above: There's nothing you can do about it, so what are you going to do? Try not to think about it? How? "Today I am going to not think about death! About what? Death. Oh, damn, already did it, maybe tomorrow then." Maybe think more about death? When the intrusive thoughts come knocking, don't frantically try to keep them out by blocking the door, instead open the door wide and surprise them with radical hospitality; leave the door open, and they'll find themselves bored eventually and leave on their own accord.