“How can I reduce the sensitivity of my teeth after whitening?”

Yes, use a sensitivity relief toothpaste before and after bleaching.

Most dentists have desensitizing gel they can give you. If not, brush with a desensitizing tooth paste. the best ones are by presription

If you have had your teeth whitened professionally in the dentist office, most likely, one has been given a fluoride treatment prior to leaving and some fluoride to apply at home. If one is using a take home whitening, a fluoride toothpaste can be used daily to reduce the sensitivity.

Hi There
Use "SENSODINE" tooth paste.

After brushing your teeth and flossing and you are ready to go to bed, apply a sensitive tooth paste like plain Sensodyne with your finger or toothbrush, spit out the extra, and go do bed. Do not wash the toothpaste off. Leave it on all night. If you rinse, you are rinsing off the very thing you want to keep on it. If you want to apply right after bleaching, that is fine, but leave it on for at least half an hour without eating or drinking. If you are bleaching with a gel, you may want to not use a bleaching rinse or toothpaste in addition to the gel. Use them after you have achieved the bleach shade you want. Realize you have to bleach a little whiter than you want, as the shade will darken somewhat after stopping. You can also space out the bleaching from every day to every second or third day, allowing the teeth to recove.

You also have to brush your teeth starting at the gumline, using a soft toothbrush, pick a side after flossing then brush BEHIND the last tooth at the gumline. Brush gently back and forth and go to the opposite side brush BEHIND that last tooth then brush your gumline where your tongue and palate are.
You have bone and tissues there
Brush your tongue and gargle

Use toothpastes which are good for sensitivity.