Living by myself

I've been living by myself since last weekend. Or: (I began living by myself last week)
I feel like going back home but I shouldn't depend on my family.
If I live with my family, I don't do any housework.
The apartment rent is expensive for me.
So I must be an excellent person who does everything like cooking, cleaning and health care by herself.

Or: (I want to be an excellent person and do everything like cooking, cleaning and health care by myself)

Where you wrote "a excellent person" i corrected it to "an excellent person".

You use 'an' instead of 'a' when the first letter of the next word is a vowel (a, e, i, o, u)

living by myself

I've begun living by myself since last weekend.
I feel like going back home but I shouldn't depend on my family.
If I live with my family, I don't do any housework.
The apartment rent is expensive for me.
So I must be a excellent person who do everything about cooking,cleaning and health care by myself.