Are you

>!Smallpox?

Pain is what I will attack you with,
A plague that appears once, what a myth.
>! Smallpox is a painful disease which spreads like a plague

In your throat I'll sequester, Now in your hands I'll fester.
>! Smallpox starts its infection in the throat then moves to the skin

For if you see me lying around, Unbelievable pain will take you down.
>! Possibly a reference to 'smallpox blankets' in American history.  Once touched, the painful disease was easily communicable

Let's, not forget, if I touch you, you can't run away.
>!Once you have the germs, you can not get away from the disease

Title: Don't confuse me with the one about chickens!
>! Not to be confused with chicken-pox, a much less serious disease