All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Such incidents are considered from the point of view of infringement; if the pedestrian violated the rules of traffic and did what caused the injury to him, while the driver did not transgress nor was negligent by over speeding for example, or by being heedless and did not watch the road, then there is no liability on the driver.
However, if the pedestrian did not violate the rules of traffic and it was the driver who violated the rules of traffic, then he is a liable (i.e. he guarantees any damage or injury caused).
It is useful to state here the decision of the Council of the International Islamic Fiqh Academy on traffic accidents and their consequences; the resolution reads:
“… Accidents resulting from driving vehicles shall be subject to the provisions of offences established in Islamic Sharee’ah, albeit mostly done by mistake. The driver is liable for the damage that he causes to others, whether in the body or the wealth, if its features such as error and damage are fulfilled, but he is exempted from liability in the following cases:
A. If the accident resulted from a force majeure that cannot be repelled and the driver was unable to avoid it. This is any incidental matter out of one’s own control.
B. If it was because of the act of the harmed person, which has a strong influence in causing the result.
C. If the accident is caused by the fault of a third party or due to his violation, then it is the third party who bears the liability.
3. The traffic accidents caused by animals on the roads: their owners bear the liability regarding the damage caused by the animals if they [the owners] were negligent in controlling them; it is the court (judiciary) that decides on the matter.
4. If both the driver and the injured person share the responsibility of the accident, then each of them is liable according to the extent that of his share, either in causing death or material damage.
5. A. Taking into account the details of what will be mentioned in the following, in principal the one who is directly does the damage is the guarantor even if he did not transgress (violate), and the one who was the factor in causing the damage (an accomplice) does not guarantee unless he transgresses or is negligent.
B. If both the one who directly did the damage and the accomplice [one who indirectly caused it and was a factor in causing it] are joint causers, then the liability falls upon the one who directly did the damage and not the accomplice, except when the accomplice has transgressed and the one who did the damage did not.
C. If two different reasons are met, each of which has an effect on the damage, then each of those who caused the damage are responsible (liable) according to the proportion of their impact on the damage. If they are equal or that the proportion of their respective effect it not known, then they are both equally liable for the damage.” [End of quote]
Therefore, dear questioner, you should look at what we have mentioned, then based on it, if it appears that your brother was negligent, then he is liable for the damage caused to that child. In which case, it is on obligation on you to give him (the child) his right by looking for his guardian and giving it to him even indirectly if you fear to be harmed if you approach him directly. However, if it appears that your brother was not negligent, then he is not liable.
As regards whether or not you were right not to stop, then in principle you must have stopped and not fled away. However, if you were afraid to be harmed, like to be beaten as you mentioned, then we hope that there is no sin on you. What is important now is to look at what we have mentioned about the liability: if you are liable and a guarantor, then you are obliged to give him his right, otherwise you are not.
Allah knows best.