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
———————
Edit: you are actually
Coxsackie Virus (hand foot and mouth)
Pain is what I will attack you with, A plague that appears once, what a myth.
A painful disease, especially for adults
In your throat I'll sequester, Now in your hands I'll fester.
Coxsackie starts its infection in the throat then moves to the skin
For if you see me lying around, Unbelievable pain will take you down.
This disease keeps you from walking when it spreads to your feet
Let's, not forget, if I touch you, you can't run away.
you can barely walk, nevermind run with this disease
Title: Don't confuse me with the one about chickens!
Not to be confused with chicken-pox
fun (not fun) bonus: I've had this. It's awful.