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What is the difference between loudness and shrillness?

Shrill refers to a very high pitched noise, the sound wave would thus have a higher frequency. Shrillness mean producing a high, thin, piercing tone/high-pitched sound

example - crying infants, While 

Loudness: Loudness is the measure of response of a sound by a human ear. It can also be called intensity of sound.
The loudness of a sound is directly related to the square of its amplitude. A loud sound has larger amplitude as compared to a soft sound.

 

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 Loudness is a function of the sound wave's amplitude of the sound pressure. Aour ear drums are moved by the sound pressure.The greater the amplitude, the greater the volume. 
Pitch is related to its frequency. The higher the frequency, the higher the pitch. 

Loudness = amplitude of the sound pressure 
Softest sound 
Loudest sound 

Pitch = frequency 
Lowest pitch 
Highest pitch

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