My Childhood Memory.

When I was 4 years old, I was playing with my elder sister at a park while my mom was getting stuff at a supermarket. There was a high slide there. Going up the steps stairs, (stairs are inside a building) my sister tried putting her leg between fence guard rails at the top of the slide. However, one of her legs got stuck in between the fence rails. Being frightened, she started to scream. Then she asked me to go get our mom. At the time I was too panicked to think clearly normally so I rode my tricycle to go to the supermarket. As you know the tire of tricycle tyres are really is so small. Obviously, running was would have been faster. Not thinking any of it, I was pedalling as fast as possible with a stern expression serious face. Arriving at the supermarket finally, I found my mom. Then we hurried to the park. After the rescue, my mom suddenly  burst out laughing into laughter out of the blue. She told me that remembering me riding my tricycle in a emergency situation, she just couldn't help laughing.

My Childhood Memory.

When I was 4 years old, I was playing with my elder sister at a park while my mom was getting stuff at a supermarket. There was a high slide there. Going up the stairs, my sister tried putting her leg between the fence at the top of the slide. However, one of her legs got stuck in the fence. Being frightened, she started to scream. Then she asked me to go get our mom. At the time, I was too panicked to think normally so
I rode my tricycle to go to the supermarket. As you know,  the tire of a tricycle is very small. Obviously, running was faster. Not thinking straight, I was pedaling the trycicle as fast as possible with a serious face. Arriving at the supermarket finally, I found my mom. Then we hurried to the park to rescue my sister. Sometime later, after the rescue, my mom burst into laughter out of the blue. She told me that remembering me riding my tricycle in that emergency situation, she couldn't help but laugh.

My Childhood Memory.

When I was 4 years old, I was playing with my elder older  (elder is ok! but, elder sometimes sounds very formal, so I think "older" sounds more natural. ) sister at a park while my mom was getting stuff at a supermarket. There was a high tall slide there. Going up stairs, my sister tried putting her leg between fence at the top of the slide. However one of her legs got stuck in the fence. Being frightened, she started to scream. Then she asked me to go get our mom. At the time I was too panicked to think normally so
I rode my tricycle to go to the supermarket. As you know the tires of tricycles is  are so small. Obviously, running was faster. Not thinking about this any of it, I was pedaling as fast as possible with a serious face. Arriving at the supermarket finally, I found my mom. Then we hurried to the park. After the rescue,  out of the blue, my mom burst into laughter. She told me that she remembered ing me riding my tricycle in an emergency situation, and she couldn't help laughing.

英語は上手と思う！軽やかな間違いだけ。凄い！

Your English is very good! You made only minor mistakes, but your conversational ability seems pretty good, and sounds mostly natural. Keep practicing!

Some notes:

You can use the word "elder", it's not wrong. I suggested "older" because it sounds less formal. 

You can say "I took my tricycle to the store" instead of "I rode my tricycle to the store". "rode" is ok, but you can also say "I took my car to the mall" or "I took my bike to school".

You can also consider using "all of a sudden" instead of "out of the blue", but both are ok.