Sickness is not mentioned in the 2nd noble truth. The 2nd noble truth mentions three types of craving, namely, craving for sensual pleasure, craving to be & craving not-to-be as causes of suffering.
The 2nd noble truth explains suffering arises in relation to sickness due to craving not-to-be sick.
Of course, there is karma, child is sick because of previous karma.
Previous karma does not create sickness. Sickness is created by virus, bacteria, etc. For example, a person might get sick because of the negligent kamma of not taking a precaution, such as not wearing a condom when having sex. But the sickness is created by bacteria and not by kamma. For example, modern people who have lots of promiscuous sex do not get sick as often as they used to because of modern medicine. Where as in the past, promiscuous sex resulted in people dying from syphilis, gonorrhea, etc. This shows sickness is not caused by kamma.
A child gets sick because of bacteria or because of the negligent kamma of its parents that results in the child contracting a bacterial infection.
Mostly we have a very detailed description of the 1st noble truth: life is suffering (sickness, death, old age, the whole life
disappointments, departures, not getting what person wants, losing
The 1st noble truth does not say life is suffering. The 1st noble truth summarised all suffering as attachment to the five aggregates. Sickness is include here because it is common for people to suffer about sickness. But it is due attachment to sickness that people suffer, namely, craving not to be sick. Sickness itself is not suffering. The Buddha got sick but did not suffer when the physical body was sick.
In Buddhism, there is physical sickness & mental sickness. The 2nd noble truth is about the arising of mental sickness (dukkha). Please read SN 22.1, which states when the body get sick, to not allow the mind to become sick.
So it is, householder. So it is. The body is afflicted, weak & encumbered. For who, looking after this body, would claim even a
moment of true health, except through sheer foolishness? So you
should train yourself: 'Even though I may be afflicted in body, my
mind will be unafflicted.' That is how you should train yourself. SN