Not Medical Advice:
We checked with Crest, the makers of 3D Whitestrips, about using the strips over night and their information is "do not wear Whitestrips overnight or while sleeping."
One of the reasons, as you found, is that it can cause increased sensitivity.
You might consider taking a break for 2 to 3 days to let your teeth recover. WebMD also suggests asking your dentist or pharmacist for a high fluoride-containing product, which can help remineralize your teeth, and to try using a toothpaste that contains potassium nitrate, which can help soothe the nerve endings in your teeth.
Crest also offers a great page full of Teeth Whitening Tips: Don’t Believe the Myths.
In the news, Crest maker Procter & Gamble is set to release a brand new product in September called Crest Sensi-Stop Strips which will provide what P&G CEO A.G. Lafleya calls “tooth sensitivity relief like never before.”