I'd say go to a differrent hospital or a private rehab center if you are concerned about your relationship with coworkers. However, lying ( or withholding ) info from your primary care physician is not really Helpful in the long run either.
I am assuming that if you work in an ER you've seen some of the possible complications of withdrawals, so I'm glad you are seeking medical assistance.
Think of what advice you would give a patient under your care that was in the same situation you are.