If you're using your camera/lens near their maximum capabilities you need to nail the exposure if you want to minimize noise.
As mentioned the photo of the child is badly under exposed.
You do not say what metering mode you used, nor if when you added ISO so you could speed up the shutter if you added sufficient ISO.
If you added 2 stops of shutter speed, you needed to add 2 stops of ISO to keep the exposure the same.
If the light meter in the camera is indicating under exposure you have needed to add a 3rd stop of ISO.
In case you don't know what a 'stop' is and how it relates to the triad of exposure adjustments.
A Stop
A stop is a fundamental photography concept.
A 'stop' is a doubling (2x) or a halving (0.5x) of the amount of light that reaches the recording media, be it film or an electronic sensor.
A stop change in exposure can apply to shutter speed, lens aperture, and/or ISO.
Since exposure is a triad of adjustments (shutter speed, ISO, lens aperture) you can change 1, 2 or all 3 of the triad settings.
If you want 1 more stop of exposure (brighter) you can adjust just one of the 3 by 1 more stop.
Or, you can change 2 of the 3 by 1/2 more stop each for a net gain of 1 stop of exposure.
Or, you can adjust all 3 by 1/3 more stop for a net gain of 1 stop of exposure.
You can also change the triad of settings and have no change in the exposure.
If you change 1 of the 3 settings by 1 stop more exposure and change a 2nd setting by 1 stop less exposure the net change is zero.
Suppose you subtracted a stop of shutter speed to help stop subject motion, you could add a stop of lens aperture to keep the exposure the same. However, adding a stop of aperture will also affect the total DoF by a small amount. So, if you don't want the DoF to change you would add a stop of ISO instead, however, adding a stop of ISO will increase by some amount the image noise in the photo.
Note: DSLR cameras are set by default to adjust the exposure settings in 1/3 stop increments.
Most DSLR cameras let you change that to 1/2 stop or 1 stop increments.
However, the advantage of 1/3 stop step increments is more precise control of exposure.