Near my house

It has been a year since I moved to here, but I have been lived a life without walking around my house, because I am busy. but because I am busy I do not normally get to walk around the area.

There is a hospital Near my house.

You don't have to capitalize "near".

When I walked near there, I saw some people smoking.

This sentence is fine but it might sound more natural to say: I saw some people smoking near the hospital.

I am was surprised.

Past tense. Since you are describing something in the past.

"I got injured my right foot with in a car accident last week.

"Injured" can be by itself.

It has only been only three days since I entered came to this hospital, but I feel bored now am already bored."

If you put "only" after "has", it emphasizes "only." Also, normally we just say "I am bored", not "feel bored."

It has been a year since I moved to here, but I have been living a life without walking around my house, because I am busy.

so keep in mind when you want to talk about when you moved some where its more proper to say "it has been a year since i moved here" how you have it written now, it would be proper to say " it has been a year since i moved to (the place you now reside)" for example, "it has been a year since i moved to houston"

"I got injured my right foot with a car accident last week.

in this part you wouldn't say "i got injured my right foot..." you would say "i have injured my right foot..."

It has been a year since I moved here, but I have been living my life without walking around my house, because I am too busy.

I was surprised.

Then, they talked to me.

"I injured my right foot with a car accident last week.

It has been only three days since I entered the hospital, but I feel bored now."