After Havdalah do I have to say a blessing of Shehakol on water that I am drinking right afterwards?
You must recite a Shehakol over the drinks you have after Havdalah if you did not have any wine to drink after Havdalah, such as you heard Havdalah from another, or said Havdalah but gave it to a child to drink as is customary on Motzei Shabbos Chazon.
Explanation: The law is that the blessing of Hagafen on wine exempts the blessing of Shehakol on all other liquids that are present at the table, or one had in mind to drink, at the time of the blessing. The reason for this is because wine is the head of all drinks, and therefore it is the main drink regarding a blessing and all other drinks are secondary to it. However, this only applies if one actually drank wine. If, however, one heard the blessing from another person but did not drink wine, then he cannot fulfill his obligation over a Shehakol beverage with this Hagafen that he heard, just like one who said Hagafen over water does not fulfill his obligation. This applies even by Havdalah, as although the sages allowed one to fulfill his obligation of Havdalah by simply hearing the blessings, this is very different than the laws of Birchas Hanehnin which requires that one actually drink wine to be exempt from saying a blessing on other beverages.
Sources: See regarding the general rule that hagafen exempts all other drinks: Seder 1:21; Luach 5:11; Admur 174:4 and 7; 204:12; 272:13; Michaber 174:2 and 208:16; Rabbeinu Yona Brachos 29a; Rosh Brachos 26; Rebbe Chiya in Brachos 41b; Ketzos Hashulchan 53:13 and 60:7; M”B and Kaf Hachaim on 174 and 208 ibid; Piskeiy Teshuvos 174:1-7; See regarding that if one heard Kiddush but did not drink any wine, then he must recite a blessing over other drinks: Derech Hachaim Hilchos Kiddush 71:8; M”B 174:3