Hope its fine making a thread cause the stupid questions one is about to die.

I was taking my freshly bought Canon 70D (Kit lens 18-55 IS STM, should be completely new) for a spin and ended up scrambling to take this picture to catch the cyclist, which made me screw up the shutter speed underexposing the picture. I do expect some noise trying to recover it, but what worries me is all that color-noise you can see in the excerpt to the right, which i increased the exposure of in lightroom to make it more evident.Those bright pixels are all over the darker areas of the picture. Is this normal? If so, why is it making this much noise? because of underexposure fuckign with the sensor or something? Or did i somehow get ripped off and got a broken sensor or something.