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Dear John,
How are you? I’m writing to tell you that I took part in swimming competitions , at my school.
I did that only because I really like to swim and I wanted to check out. You imagine , that won first place.
Un fortunately , the event started with some troubles. I have forgotten cap. Luckily , my friend had her swimming things and I could borrow it.
My friends cheered me on and carried me around swimming pool. It was amazing.
Hope to hear from you.
Love
XYZ

Dear John,
How are you? I’m writing to tell you that I took part in swimming competitions <--W WIELU? , at my school.
I did that only because I really like to swim and I wanted to check out<--ZLE WYRAZENIE. You imagine , that won first place.<-- TO ZDANIE ZUPELNIE ZLE, TRANSLATOR?
Unfortunately , the event started with some troubles. I have forgotten <-- ZLY CZAS+DAJ "WZIĄĆ"+PRZEDIMEKcap. Luckily , my friend had her swimming things<--CO? and I could borrow it.
My friends cheered me on ON ME and carried me<-- NA TACZCE? around PRZEDIMEK swimming pool. It was amazing.
Hope to hear from you SOON.
Love
XYZ

czy teraz dobrze proszę sprawdzić
Dear John,
How are you? I’m writing to tell you that I took part in swimming competition , at my school.
I did that because I really like to swim and I wanted to check up.
Can you imagine , that I won first place.
Unfortunately , the event started with some trouble.
I didn't took a swimming cap. Luckily , my friend hasn't started the competition, so lent me it.
Unfortunately , the event started with some troubles. I have forgotten cap. Luckily , my friend hasn't started the competition, so lent me it
My friends cheered with me and they carried me around a swimming pool. It was amazing.
Hope to hear from you.

can you imagine that I won the first place - ok
reszty nie poprawiłeś

Dlaczego 'cheered ON ME' a nie, tak jak on już ma, 'cheered me on'?

pomylilem sie

Dear John,
How are you? I’m writing to you to tell you that I took part in a swimming competitions at my school.
I did it only because I really like to swim and I wanted to check how good I am ? Can You imagine - I won the first place!
Unfortunately , the event started with some troubles. I have forgotten my cap. Luckily , my friend had his swimming gear and I was able to borrow it.
My friends cheered and carried me around swimming pool. It was amazing.
Hope to hear from you.

a tak jak wyżej jest Ok ?

I’m writing to you to tell you that I took part in a swimming 'competitions' (tutaj masz l. mnoga, a wczesniej przedimek 'a' - albo jedno albo drugie) at my school.
I did it only because I really like to swim and I wanted to check how good I 'am' WAS ? Can 'You' (you - mala litera w srodku zdania) imagine - I won 'the' (wg mnie bez tego 'the') first place!
Unfortunately , the event started with some 'troubles' (za silne slowo, tutaj mozna 'mishaps). I 'have' (HAD - czas przeszly) forgotten my cap.
My friends cheered and carried me around (brak przedimka) swimming pool.

Popracuj nad przedimkami (a, an, the)