I am going to get further study in Hong Kong.

I have never been to Hong Kong before, but I want to get further study there, because I want to
experience a different educational environment.
I have applied for some masters programs three months ago. Now I have got three offers. I think
I will probably go to study in Hong Kong Baptist University and will major in Education. I am going to be
an intern in Guangdong Experimental High School, where I would love to work after graduation.

[Very good work.  "I have applied" refers to an unspecified time in the past.  Since you specified the time ("three months ago"), it should be "I applied" (simple past).