I have studied in English, especially speaking, for 2 years. I have studied English, especially speaking, for 2 years.

Until recently, I didn't knowrealize that themy skills were not enoughlacking. Until recently, I didn't realize that my skills were lacking.

This sentence doesn't make sense with the rest of what you wrote: This sentence sounds like you just realized that your skills aren't very good, but the rest of the journal is about how excited you are that you had a successful conversation in English.

Yesterday, at work I had a chance to speak with a native speaker at work. Yesterday at work I had a chance to speak with a native speaker.

During conversation, I knew that I could listen to his sentences,realized that I was able to understand him and speak with him. During conversation, I realized that I was able to understand him and speak with him.

It made me really excisted that my study gave me a small but good resultwas paying off in this small but significant way. It made me really excited that my study was paying off in this small but significant way.

It's time to keep at it for. I want to continue practicing to speak ing English. It's time to keep at it. I want to continue practicing speaking English.

"Keep at it" is a great phrase but it is usually not followed by anything.