It tells us the winner when equines do race.
To my misfortune there's one on my face.
Our countries have many, some say full of gas.
My sister was one when completing her class.
Sometimes it's level, sometimes it's not.
The coin in my hand, just one has it got.
Up at the top it starts a great flow.
The one on my face is ready to blow.
I believe it's
head.
It tells us the winner when equines do race.
Horse races can be won "by a head."
To my misfortune there's one on my face.
Referring to acne; i.e., a whitehead or blackhead
Our countries have many, some say full of gas.
Heads of state are often not well-respected.
They could also be considered airheads. (Thanks to @feelinferrety.)
My sister was one when completing her class.
The head of the class is the top-performing student.
Sometimes it's level, sometimes it's not.
People can be level-headed, sensible, and can also not be.
The coin in my hand, just one has it got.
A coin often has one tail, and one head.
Up at the top it starts a great flow.
The head a river is its source.
The one on my face is ready to blow.
Acne again?
Oh, I just got the title: Figure this out while I relieve myself
Head is another term for toilet, where one can relieve oneself.
