Should I still go to work if I have bell's palsy?

Maybe. Bells palsy typically resolves within a few weeks to months. In the mean time, you need to be sure to prevent your eye from drying out, as your eyelids may be unable to fully close. If your vision is blurry or your eye is painful see an eye doctor.
No problem. Bell's palsy affects you only and cannot be spread to your coworkers. If the dysfunction from your palsy does not interfere with your work duties, by all means go back to work. Even if your job involves greeting the public most people are very tolerant of a problem in those they have to deal with. Just be upfront with why your appearance has been altered.