I think he might have, if he had been even reasonably sure that what he was sensing was indeed the Ring. It's not clear he did: "... for a moment he was troubled, sensing some other power within his valley." But that could have been anything, I suppose. He appears to have tried to check whether it was the Ring:
[Frodo] felt, more urgent than ever before, the command that he should put on the ring.
Presumably this command comes from the Witch-king. But he is frustrated, partly by Frodo's choice to grasp the Phial of Galadriel, partly perhaps by the cloaks of Galadriel. In addition, he's rushing to fulfill Sauron's command, and he doesn't have enough proof of what the problem is to justify overriding that.
(Both quotes from The Two Towers, Chapter VIII, "The Stairs Of Cirith Ungol".)
As far as "the Witchking could have ordered 2 or 3 nazguls to look around" - I don't have my book with me at the moment, but weren't the other Nazgul engaged in Gondor (at Osgiliath and Minas Tirith) at the time? It would have taken them a while to fly over; the Witch-king might have found it more efficient and quicker (as @PaulGriffiths points out) to alert an Orc patrol, who had more manpower and could search or guard the area better.