The Prophet (sallAllaahu `alayhi wa sallam) is reported to have drunk Zamzam water, carried it and encouraged muslims to drink it. He said, "Zamzam water is (good) for what one intends to achieve by drinking it".
As narrated by Ibn `Abbas, the Prophet (sallAllaahu `alayhi wa sallam) came to some drinking water providers and asked for a drink of water, at which time Al-Abbas instructed Fadhl, "O Fadhl, go to your mother and get the Prophet a drink , but the Prophet (repeated) to the providers, "Give me a drink of water". Al-Abbas said,"O Messenger of Allah, they put their hands in it." The Prophet (sallAllaahu `alayhi wa sallam) repeated "Give me a drink" (When given the water), he drank it, then went to the the Zamzam well, where the drinking water providers were drawing water, and working with it. He said to them, "Continue, for indeed you are upon righteous action" and added, "If it were not for the fact that you would be overcome (i.e. by people wishing to emulate my action), I would come down and put the rope (on my shoulder and pull to draw water with you)
Also, as narrated by Ibn Abbas, the Prophet (sallAllaahu `alayhi wa sallam) said "Zamzam water is good for that which it is (intended to be)drunk for. If you drink it to satisfy your hunger, Allah will satisfy your hunger. If you drink it to quench your thirst Allah will quench your thirst. Jibreel dug it (the zamzam well) for Isma'il (Ishmael) to drink from."
As reported by Aisha, she used to carry water from zamzam and so did the Prophet (sallAllaahu `alayhi wa sallam) as was collected by At-Tirmidhi, like other ahaadeeth that have occured concerning the virtues and blessings of Zamzam water.
Though some of the hadeeths on Zamzam are questionable , they are judged by some scholars as saheeh(authentic) and they have been acted upon by the Companions and that which they indicate have been acted upon until the present day.
This is likewise supported by that which was collected by Imaam Muslim in his saheeh that the Messenger (sallAllaahu `alayhi wa sallam) said concerning Zamzam "It (zamzam) is blessed water and good food". Abu Daawood's version of the hadeeth states "It is blessed water, good food and healing from ailment."
There is no evidence to suggest that the Prophet (sallAllaahu `alayhi wa sallam) did any recitations on water from the well of Zamzam for any of his Companions to drink or massage with, for a particular reason or for the sake of healing - even though he was plentiful in blessings, has a lofty station, benefited (everything) generally, and having ardent desire for good for his ummah.
Likewise with him repeatedly visiting Zamzam before Hijra, his numerous performances of `Umra and Hajj to the Sacred House after Hijra, it is not established (in any of that) that he guided his Companions to recite upon him even though it was compulsory upon him to convey and clarify (the truth) to the ummah
Thus it can be concluded that if recitation on Zamzam water for the mentioned purposes were allowed, the Prophet (sallAllaahu `alayhi wa sallam) would have done it and conveyed it to the ummah, for indeed there is no good except that he guided his ummah to it and there is no evil except that he warned his ummah from it.
However there is nothing that prevents recitation upon it as is the case with ordinary water for healing purposes,(in fact) Zamzam water should be given precedence, because of its blessed nature and healing qualities as reported in the above mentioned ahadeeth.