The use of a Waterpik should not make your teeth or gums sensitive.
However if you use the Waterpik at the wrong angle then you may experience some discomfort or pain with the use of the Waterpik.
You may already have sensitive teeth and not know about is so if you notice any pain or other discomfort from the use of the Waterpik I would recommend seeing a dentist to have your teeth checked out.
The use of a Waterpik to clean your teeth should not damage your teeth or gums.
That is unless you have really sensitive teeth or gums and if you do have more sensitive teeth or sensitive gums then it could be possible for the Waterpik to damage your teeth and gums.
I use a Waterpik myself and have not had any problems or damage done to my teeth or gums by the use of the Waterpik.
I also make sure to brush my teeth daily and even use a regular string floss to floss my teeth and use the Waterpik every few days or so.
The Waterpik is safe to use on your teeth and for your gums and should cause you no harm.
If you notice bleeding of the gums or problems with your teeth when using the Waterpik then you could have some other problems such as gum disease, gingivitis etc.
Or you may be using the Waterpik wrong.