Crying infants and respiratory rate

Sick infants cry, some sick infants have increased respiratory rate. Assessment of respiratory rate is important for identifying the disease and assessing the general wellness of the child. This is pretty difficult to do when the infant is crying.
This led me to wonder if the rate of vocalising?/phonation? while crying can be a surrogate for respiratory rate?
This does sound a little absurd, but crying involves respiration, inhalation and phonation, so wouldn’t it be logical to expect some relation between respiratory rate of a non-crying infant and the crying rate of the same infant?
On another note, isn’t crying pretty useless while an organism is in respiratory distress? Crying seems to be useful only if it can attract a solution to the problem that led to crying. So would species with more attentive adults be more likely to have crying young ones than species with adults that leave the young ones faster?

Anyways, do let me know if anyone finds a correlation between crying rate and respiratory rate in a child.