"Banging my head against a brick wall"

I wonder if people really do this?

On saying that I know Ive done it once, years ago I had an infection in my gums and the pain was so intense that the thought of banging my head ON a brick wall seemed more appealing then suffering the pain in my gums, hence I did it and yes the pain on my forehead took my mind of the pain in my gums, the bruise I was left with was very unsightly and the pain in my gums was still there 30 minutes later..... so it solved a problem for a short time but didn't solve it in the long run.
So I got to thinking yesterday, why and where does this expression come from and was it really thought of in the contense in which we use it.

I looked it up ......

be banging/hitting your head against a brick wall

to keep asking someone to do something which they never do "I've been trying to get the rules changed for years now but I'm hitting my head against a brick wall. He never listens to me - sometimes I feel like I'm banging my head against a brick wall."

I feel like I'm banging my head against a brick wall
meaning, despite my best efforts I am making no progress/cannot make a breakthrough.

I feel like this a lot.

But then I looked at in in a different way, what if the person you where trying to change couldn't or didn't want to, and they felt like banging their head against a brick wall cause all you where doing was nagging at them and trying to change them.

And if they did it, literally banged their head against a brick wall would this be self harming?.
I'm sure Bip and Bop feel like this some days, I'm sure the wall looks so appealing or would feel better than me going on at them about the same thing everyday, I'm almost sure that they walk away thinking "I just wish she would stop" and I have to say I don't blame them, there are times I sound like a broken record.
They don't bang there heads on brick walls literally, or at lest Ive never witnessed this action, but I have witnessed them harm themselves in other ways.
Example: Bip use to very frequently hit himself when he did something wrong, this doesn't happen so much now, he did do it the other day when he pulled a silly move with something and I just gave him my look and he stopped. The smack he would give himself used to be a very hard on almost a punch in the head action, and there would never be any tears with pain, and lets face it it hurts when you punch yourself in anger, and it was a good smack he would give himself cause it always left a red angry mark.
Bop doesn't punch herself, she picks at her skin until its red and bleeding and it doesn't stop there she will then continue to pick at the same red sore spot for days sometimes week not allowing it to heal.
To me this is a form of self harming, which if not dealt with with turn into something bigger and nastier, in years to come.
I don't fully understand self harming, I'm not a great lover of pain and self inflicted pain, oh my goodness I just couldn't do that to myself on a daily basics. I'm not sure if its cause I respect myself, love myself or what it is I just don't have it in me to mutilate myself, so you could say I don't understand this at all, which makes me feel very unqualified to deal with the situation of self harming all I know is it could escalate into something terrible.
Its hard when you know what something is but have no idea why it happens or how to deal with it.
I did find a site which I will be scouting through to try and get some insight as the times goes on and I'm sure there are other sites out there which might help me understand this situation more.