DuringI didn't go away for those holidays, I didn't get away.

I think this might be the most natural way to convey your message.

I stayed at home because my mother got injured at her leg so she couldn't ski and ithis meant that we wouldn't be able to go skiing with my cousins oin the south of France.

Obviously, I was a little sad, because skiing is one of my favorite hobbies, but I decided to take advantage of that situation by seeing my friends, work fordoing school work and improveing my skills, likefor example by improving my English or guitar skills.

My last holidays ended up was 3 years ago, and I keptstill have a really good souvenir of themfrom it.

Sometimes, I feel like it's a good thing to just rest, get a refillreset, and spend time alone.

I think 'refill' is more often used in the context of beverages.

The only problem was that I had a test right before the holidays, andwhich I thought I failed it, so ithis disturbed me for a while (I received my grade yesterday and got 18 out of 20, the best grade of(out) of (everyone in) the class, so it was finalultimately a success!).

However, I managed to distract me aboutyself from that thought by watching the winter Olympic Games.

During those holidays, I would watch the different sports during the evening, after hanging out with some friends or working.

It was a good way to reward me when I have beenyself after being productive or whatever.

To conclude, I had a great time during those holidays, I saw my friends and movetravelled to Paris for onea day (I'll talk about that later).

During those holidays, I didn'’t get awayo outside.

I stayed at home because my mother got injured at her leg soa leg injury. As a result, she couldn't ski and it meant that we wouldn't go skiing with my cousins on the south of France.

Obviously, I was a little sad, because skiing is one of my favorite hobbies, but I decided to take advantage of that situation by seeingthe situation as an opportunity to see my friends, work for school, and improve my skills, like improving mysuch as English orand guitar skills.

My holidays ended up 3 years ago, and I kept a really good souvenir of them.

Sometimes, I feel like it's a good thing to just rest, get a refillrecharge, and spend time alone.

The only problem was that I had a test right before the holidays, and I thought I failed it so it disturbed me for a while (I received my grade yesterday and got 18 out of 20, best grade of the class, so it was finally a success!).

Congratulations!

However, I managed to distract me aboutyself from that thought by watching the winter Olympic Games.

I loved watching them doing freestyle figures and artistic skating.

During those holidays, I would watch the different sports during the evening, after hanging out with some friends or after working.

It was a good way to reward me when I have been productive or whateveryself after a productive day or something.

“or something” sounds better than “or whatever”

To conclude, I had a great time during those holidays, I saw my friends, and moved to Paris for one day (I'll talk about that later).

Please tell me what you though ofink about my English and feel free to give me some advice!

During those holidays, I didn't get awayo anywhere.

Or 'I didn't go away'

I stayed at home because my mother got injured at her leg so she couldn't ski and it meant that we wouldidn't go skiing with my cousins oin the south of France.

Don't need the 'at' in 'injured at her leg'.
You would say 'my mother got injured' if you don't want to mention which body part.

Obviously, I was a little sad, because skiing is one of my favorite hobbies, but I decided to take advantage of thate situation by seeing my friends, doing work for school and improveing my skills, like improving my English or guitar skills.

'seeing', 'doing' and 'improving need to have the same conjugation if you're listing activities.

Sometimes, I feel like it's a good thing to just rest, get a refillrecharge and spend time alone.

'recharge' is a better word here, or maybe 'refill my energy'

The only problem was that I had a test right before the holidays, and I thought I failed it so it disturbworried me for a while (I received my grade yesterday and got 18 out of 20, best grade of the class, so it was finally a success!).

'worried' fits better here. 'disturbed' is more intense and refers to something more unsettling.
(Congratulations!)

However, I managed to distract me about that thoughtdistracted myself by watching the winter Olympic Games.

Don't need the 'managed to'.
'myself' instead of 'me'

I loved watching them doing freestyle figures skating and artistic skating.

During those holidays, I would watch thed different sports during the evening, after hanging out with some friends or working.

It was a good way to reward meyself when I have been productive or whatever.

To conclude, I had a great time during those holidays, I saw my friends and moved to Paris for one day (I'll talk about that later).

'saw' and 'moved' need to be in the same tense

Please tell me what you thought of my English and feel free to give me some advice!