Starting my new life

This February, I came to this country, USA. Actually, I didn’t want to move here—I had a great job and all of my friends and family are in China. after 3 months of talking with my husband who hadhave decided to work here for 5 years—I eventually gave up my life in China. Since I have been here out of the gate, I have found my life to be a bed of thorns. But I believe I will get there as long as pursue my aims with diligence.
Fortunately, I could take an advantage of my major to find a nursing job here with a license and good English skills. I have been working on it, including reviewing the medical professional knowledge for RN licensure, taking ESL classes to improve my language skills. In addition, I have been trying hard to adapt to the way of living and surroundings by taking part in group activities, making friends, finding a temporary job.
To be a research nurse in the US is my short term dream. My long-term intention is to own a pharmaceutical company where we invent new medicine and advanced therapy programs. I will stick with this until I achieve success.

你的语法似乎不是很熟练，但我相信，我语法并没有学的比你好，不过我觉得你写句子的时候，语法不太小心。

Starting my new life

This February, I came to this country, USA.

This February I moved to the US.  [what you wrote isn't wrong, but this is more colloquial.]

Actually, I didn’t want to move here—I had a great job and all of my friends and family are in China. [fine]

after 3 months of talking with my husband who have decided to work here for 5 years—I eventually gave up my life in China.  [where is here?  You mean the US, right?]

After three months of discussions with my husband, he decided to take on a five-year work contract in the US.  I agreed to give up my life in China.

Since I have been out of the gate, I have found my life to be a bed of thorn.   [These idioms aren't used correctly.  It's better to just state things directly.]

Since I got here, life has been difficult.

But I believe I will get there as long as pursue my aims with diligence.  [Get where?]

However, I believe I can make a good life for myself so long as I dilligently pursue my goals.

Fortunately, I could take an advantage of my major to find a nursing job here with a license and good English skills.

Fortunately, I can take advantage of my major, nursing license, and good English skills to get a nursing job.

I have been working on it, including reviewing the medical professional knowledge for RN licensure, taking ESL classes to improve my language skills.

I have been reviewing medical knowledge to get the RN license, and taking ESL classes to improve my language skills.

In addition, I have been trying hard to adapt to the way of living and surroundings by taking part in group activities, making friends, finding a temporary job.

In addition, I have been trying hard to adapt to life in the US, by taking part in group activities, making friends, and finding a temporary job.

To be a research nurse in the US is my short term dream.

To be a research nurse in the US is my short-term goal. [is it registered nurse?]

My long-term intention is own a pharmaceutical company where we invent new medicine and advanced therapy programs.

My long-term dream is to own a pharmaceutical company that invents new drugs and advanced therapy programs.

I will stick with this until I achieve success.

Hope that helps -- and good luck!