i was wondering how なりそう was conjugated i know it was made of なる and そう but i don't know how \ なる became なり
そう can be attached to a root verb or the continuative form of a verb. If そう is attached to the root like なる, it means it is second hand information, i.e. "I heard that something will...".
If そう is attached to the continuative form like なり, as in なりそう, it means there is primary evidence or sensation to make the statement, i.e. "it appears that it will..."
So なりそうだ would be the correct way to say "it appears it will be(come)", or よく なりそう な 時 would be "(a time) when it seems to be getting better" or something to that effect.