Is it normal to have 314 stimpacks?
I'm in the hundreds for stimpaks too.
I don't think it is unusual, since they are really really common (practically every building has a bathroom with a medkit containing 1-3 stimpaks).
Plus they weigh nothing so there is no need to store/sell them.
And you can generally heal just as well from food from creatures, and even drinking water is viable with Lead Belly.
I typically only use stims when I am taking a serious beating, healing my limbs, or healing a companion (why do stims help nick???).
But I pick them up every time.