This is drawn. White has to keep checking (while Black moves back and forth from a1 to a2) otherwise if White moves somewhere else Black plays Qh7+ and wins.
In the second diagram it still looks like it is a draw. But since you have the initiative, there are plenty of chances for your opponent to make mistakes. See the move list in the diagram below for things black can do wrong.
this was a position in one of the recent games i played.....could i have won this?
it was drawn