I'm going to share an experience that left a deep mark on my soul, and also a phrase that has helped me to overcome my sadness.

That experience was when my dog died.

I loved him, and took care of him: I bathed him, walked him, and fed him.

I took on all the responsibilities that didn't require money because I was a teenager, and I had no job.

Everything passhappened very fast in three days.

My family was devastated,. I had never seen my father cry before, and also I cried everyday in my room.

Your dog lived the best life: he traveled, saw the sea, lived in a loving home, he slept in your bed every day, ate the best food, and received kisses and hugs daily.

At that moment, I only remembered the good times we had with him, and how happy was his life was.

Those words are still in my mind, each time I saw his photos or a dog that looks like him,. I cry again, but not because I'm sad;.

Everything passhappened very fast within three days.

Taking about an event happening during a specific time period you would say 'within' instead of 'in'

My family was devastated, I had never seen my father cry before, and I also I cried everyday in my room.

In the middle of that sadness, an ex-friend tolasked me, "Why are you so sad?

Use 'asked' instead of 'told' when someone is asking a question

At that moment, I only remembered the good times we had with him, and how happy was his life was.

Those words are still in my mind, each time I sawee his photos or a dog that looks like him, I cry again, but not because I'm sad;

You could say 'each time I see' or 'each time I have seen'

I took on all the responsibilities that didn't require money because I was a teenager, and I had no job.

Just to shorten it a little you can just add "and"!

No one told me how serious it was at the time or that I could have prevented a bad outcomehis sickness with a vaccine.

Good to be a little bit more clearer here on what you mean by bad outcome! It could be his sickness or his death.

He became so sick that he couldn't recover, became so sick and died.

The sequence has to make sense!

Everything passed very fast inby really quickly in those three days.

everything passed = everything was gone
everything passed by = everything happened/took place
really quickly sounds more natural in this context.
those = to indicate the specific days, just saying three days can mean three random days

My family was devastated, I had never seen my father cry before, and. I also I cried everyday in my room.

In the middle of that sadness, an ex-friend tolasked me, "Why are you so sad?"

it is a question, so ask would be suitable for this instance.

My friend said, "Your dog lived the best life: he traveled, saw the sea, and lived in a loving home, h. He slept in your bed every day, ate the best food, and received kisses and hugs daily."

Add punctuation as well as introduce what your friend said.
Don't make your sentences too long!
The rule is always (two commas , , add an "and") then end the sentence.

My friend continued, "He was your baby.

As your friend's speech is a little long, it's good to add a part here where you specify that he continues speaking.

He lived a better life than I haveam living".

As your friend is alive and talking to you presently in this instance, "I have" wouldn't be exactly the tense I'd use.

At that moment, I only remembered the good times we had with him, and how happy was his life was.

Those words are still in my mind, eachvery time I sawee his photos or a dog that looks like him, I cry again, but not because I'm sad;

Grammar

Everything passed very fast, int took just three days.

My family was devastated, I had never seen my father cry before, and I also I cried everyday in my room.

Your dog lived the best life: he traveled, saw the sea, lived in a loving home, he slept in your bed every day, ate the best food, and received kissehugs and hugkisses daily.

"hugs and kisses" is kind of a stock phrase, so the opposite ordering sounds strange.

At that moment, I only remembered the good times we had with him, and how happy was his life was.

Those words are still in my mind, each time I saw his photoswhenever I see photos of him or a dog that looks like him, I cry again, but not because I'm sad;

Matching the tense of "see" to "cry", so the tense of the cause and effect match.

Iit's because I'm nostalgic and emotional.

Iit's because I'm nostalgic and emotional.

Capital letters aren't used after semicolons.