“Can social workers suffer from anxiety and depression?”

Of course. Social workers are also humans. Moreover, social workers who work with crises and those who have highly stressful jobs (which I believe includes most social workers) have a high incidence of anxiety and/or depression. Hopefully, they are open and proactive about receiving professional help for themselves.

Absolutely, in dealing with others' emotions and social needs social workers must continue to care for themselves. I utilize a variety of self-care such as journaling, yoga, meditation, walks, and massage to stay healthy.