How is my writing. Please review.?

I agree with Dee on a lot of levels. Your sentences are... strange. As if you're trying a little too hard to sound like an author writing a novel. At the same time, it sounds very casual. Both are not good. You also change tenses. Either stick to past tense or present, but don't use both. That little sentence with the thrusting or whatever just kind of made me laugh :/. Here:

I pulled myself (away) from him. I don't know why I did that(try not to use the word "that" if you can help it",but my legs raced down the pavement, (no comma) until I couldn't catch my breath.

"Hey! Wait' A voice came thrusting (this makes no sense and it makes me laugh) my heart to death. It's (watch those tenses) him

"Why are you picking (up) your pace (ignore the last too words >) so hard?"

I stopped dead. For a minute, I allowed the silence to pass on, until his words pierced me (the fact that it took her a minute to understand what he just said implies she's not very bright).'So, it was true'

I licked my dry lips and tried really hard to at-least have a look at him. But my eyes couldn't move from gazing down my bare feet.I noticed one of my nail paint chirped out. Why have you turned to see him? I questioned myself.

Okay, I'm sorry, but it's really difficult to correct and give my opinion when there is so much to work on. I'm not trying to discourage you, but there is quite a bit. So much so that I probably couldn't explain or write it all here. I've tried to revise it in a way that you could maybe compare the two, though my writing is hardly flawless itself:

I pulled myself away from him, desperate to escape. I wasn't sure why I did it, but I didn't stop to think about it until I'd run so hard I needed to rest.

"Hey, wait!" his voice pierced through me. It was him, "Why are you running away from me?" I tensed from where I was trying to catch my breath. It was silent for a moment.

"So it was true," he said softly. I licked my lips and tried to look at him, but my gaze was frozen at my feet.

Like I said, my writing itself is not flawless, but try to see how it's all in one tense. It doesn't switch. If you don't quite understand or you want a more thorough explanation, please feel free to email me. I'd be happy to review the whole thing and explain :) Sorry i couldn't be much more help.

It wasn't too shabby. However, a lot of grammatical issues! Some of it was hard to comprehend let alone evaluate for content. Also, make sure you stay in the same tense, you kept switching from past to present. I think you have potential, but I would work on it. I revised some of it for you so hopefully that helps to get you started:

I pulled myself away, escaping from him. I don't know why I did it, but my legs raced down the pavement until I couldn't catch my breath.

"Hey, wait!"

(A voice thrusted my heart to death. It was him. "Why are you picking your pace so hard?") *I didn't understand this part, how does a voice thrust your heart? What does that mean? Did the voice make her heart thrust or what? And what is picking your pace? I don't think that's a phrase*

I stopped dead. For a minute, I allowed the silence to pass on until his words pierced me. 'So, it was true.'

I licked my dry lips and tried really hard to at least have a look at him. But my eyes couldn't move from gazing down at my bare feet. I noticed one of my toe nails had chipped nail polish. 'Why haven't you turned to see him?' I questioned myself.

"Can't you answer me?" He cupped my cheeks gently and shook me lightly to stop me from gazing down. I looked at his magical blue eyes and his concerned frown.

"So, It was true.' His voice shook me again. Then, I don't recall what made me kiss him. I closed my eyes and let the world go back. Then, I noticed myself sobbing but at the same time enjoying kissing him.

'What happened?' He said slowly, and I felt his lips retreating back. I cried harder than my first cry that had happened when I saw this world first. I sobbed and cried hard.

'I...I wanna leave now,' I finished quickly and without hearing anything from him, I walked quickly and hailed a taxi.

Hope this helped!

Dee and Kellsey have given you good advice. Take it.

To be very honest, it is awkward. There are too many grammatical errors and awkward phrasing - a voice came thrusting my heart to death. What does that mean? How does a voice thrust?

Just tell the story like you were telling your friend.

Sorry.