ある日、私は気づいたの！人生は短いんだって！って英語でなんて言うの？

A 'realisation' is when something becomes apparent or focused in your mind. These usually happen very quickly like an epiphany and can sometimes shock people into changing the way they lead their lives.
For example if someone all of a sudden realises how short life is, they may go travelling and see the world 'before it's too late'.

I just realized that life is so short.
Life is so short and I just realized it.
Things change so quickly and life is so short.
Life is short and I'm reflecting on it.

If you suddenly think of something then you are said to 'realise' you only live once and it can be short so you should enjoy yourself and make the most of it you can express this as 'life is too short' or 'how short life is'

When you realise something, you become aware of it. Life has always been short, but what you are saying here is that you've suddenly become aware of that. You could of course also say that 'I became aware that life was short', which would mean the same thing.

'It struck me' means that you've suddenly had the realisation.

Incidentally, the word realise (spelt with an s) is just an alternative spelling for realize (spelt with a z). We tend to use realise in British English and realize in American English.

Use any of the above when casually talking about life being short.
Life can seem to be a long process, from the many years spent as a child to finally growing up into an adult. When we look back on all the years that have passed we realize that life is, in fact, short, life seems to have flown by.

Epiphany: realization
Flown by: passed very quickly, came and left quickly.

You have realized that life is short and want to explain that.
Either of the above two example statements should express that viewpoint adquately.