SAT Lawyer

An hour and 55 minutes should be plenty of time to connect at IAH even for a non-U.S. citizen without Global Entry and without Pre-Check. After clearing immigration and customs at Terminal E, do what we IAH regulars do: head straight out of the exit, ignore the opportunity to turn right for connections, take the escalator at the far left corner of the Terminal E meet and greet area to the second level, check-in at the counter for your UA flight if you haven't done so already, and re-clear security at the regular Terminal E checkpoint as if you are a normal IAH-originating passenger. That will almost always save you some time. Once airside past the Terminal E security checkpoint, you can walk to the E or C gates to catch your onward flight to NYC.

Also, rather than digging out your credit card and paying a change fee for your UA flight without trying a possibly less-costly alternative, I suggest calling UA, explaining that its Star Alliance partner NZ made a flight schedule change that causes you to arrive three hours later than originally planned, thereby making it impossible for you to make your booked UA flight, and see if the telephone agent will change you to a later flight for free as a courtesy. If at first you don't succeed, hang up and call again. Based upon past experience with flight schedule changes on separate bookings screwing up UA flights from IAH onward, I suspect you will find a UA agent who will help without charging you a change fee. It's certainly worth a shot or three.