Can I work part-time as a Social Worker with an MSW? Are there certain area's of social work where I could likely find part-time work?

A lot of social work jobs (as with so many jobs/occupations) are only part-time. E.g. you might work at a homeless shelter weekends-only or part-time every morning, etc. Same with a nursing home, assisted living facility, and more. Govt social service department jobs might be full-time only, but many other agencies only hire part-time people - charities often have no budget for "benefits." It is also fairly common to start any new/recent MSW grad part-time until they get 1-2 years of experience.

self-employed, sure.

and every child welfare agency i've ever heard of needs more people to the point that they might accept you as part time IF that part time is a specific and predictable hours/days per week rather than seasonal or intermittent.