Regular rinsing with salt-water and use of desensitizing toothpaste are some simple ways to take care of tooth sensitivity. However, if these do not work, consult a Dentist immediately.
An annual tooth checkup is necessary to make sure you are not facing any dental problems, and even if you are, treat them before they reach any critical stage.
As long as you stick to dentist-approved methods, whitening your teeth is considered safe.