How long will the pain and sensitivity last after teeth whitening with at home trays purchased from the dentist?

Hi:Sorry to hear about your pain.  Normally the sensitivity from whitening goes away in 48 hours after you stop using the products.  However, since the sensitivity is continuing avoid any cold or hot foods or drinks and use Oral Essentials Sensitivity Mouthwash and Toothpaste 3 times a day.Best,Dr. Maddahi

Really hope your pain has resolved by now, or you have found a solution. 
If not, or you are simply managing with the advice given by my colleagues below, I suggest that you keep a diary of what you are eating or drinking that causes you the most discomfort. 
Also note the type of toothpaste/mouthwash that you are using. 
Remember to keep oral hygiene sessions (flossing / brushing / mouth rinse) 20 minutes before or after you have eaten to avoid sensitising your teeth further. 
Then take the diary to another dentist for a second opinion. Even a different, more modern x-ray unit can give professionals insights that may be otherwise missed. 
Good luck getting to the bottom of your problem. 
Kind regards,
Thomas Dey, BDS, MSc

I'm so sorry you are having so much sensitivity.  Normally, after teeth whitening, your teeth should not be sensitive for more than 48 hours.  Since you are still experiencing sensitivity, visit your dentist and let him/her know.  Also, if you have been using the fluoridated toothpaste and mouthwash, discontinue the use of those products because in some people they can become an irritant.  Stay away from food and drinks that are hot or cold (stick to room temperature foods).  Also, stay away from acidic foods like oranges, pineapples, etc.