This is a difficult question to answer. Long story short, yes, it is possible for someone with little to no health care or social service experience to receive an offer of admission to an MSW/MPH program. As you probably already know though, the likelihood may be low (even with your grades) if you do not provide the admissions committee with some basis for trusting that your values and knowledge base align well with a possible career in social work/public health.
Often times, volunteer experiences are not named as such on an application, when in fact an applicant does actually have some volunteer work under her/his belt. You mention your dedication to benefiting your own community; were you ever involved in organizing a community event, working on a grassroots project, or been active in a student organization? These are examples of activities that are often not included on an application as "volunteer work," when in fact they should be. I would, of course, also include your experiences as a single parent, particularly if these influenced your decision to consider a change in career paths.
If there is absolutely no volunteer and/or paid social service/health-related experience you can draw on, I would strongly recommend that you consider getting some prior to seriously considering an MSW/MPH, even if you do happen to receive an offer of admission. I do understand that you come with significant experience in a different area, and you are tied up with parenting responsibilities, but it is really crucial to have some understanding of working with people/communities in a social service capacity before actually committing to a career in this area. Inexperienced MSW students are sometimes really caught off guard in their placements when they realize that their visions of social service work had nothing to do with the actual realities of working in this field (yes, even when areas of interest are macro-level/development/public health-related).
When I say it is crucial to gain some experience in related areas of work, it really doesn't mean there has to be a significant time commitment. It could be volunteering for 2 hours a week at a hospice society, long-term care facility, youth drop-in centre, or women's shelter. If you do want to pursue a career that will give you a greater understanding of human rights, these ground-level experiences are a total necessity, as they not only give you insight on day-to-day experiences of marginalization, but they also show your commitment to an area of work that (although rewarding) can be incredibly difficult and taxing, regardless of whether you work at the micro, mezzo, or macro level. If it is something like a two hour a week commitment, think of it like a two-credit course that (I believe) is an absolute prerequisite to even considering the MSW.
If you strictly want to work at the macro/policy level, without necessarily having to interact with people, you could always consider a Master of Public Policy, or a combined MPP/MPH, or a Master of Health Administration. Even macro-level social workers who work in community development often have some direct interaction with individuals whose lives will be affected by policies/programming being developed, as community consultation provides a foundation for this type of work (hence my "absolute prerequisite" comment earlier ).
Anyway, sorry for the long answer. Basically, yes, you have a likelihood of getting into a program without any volunteer experience, but (a) try to identify some aspect of your past experiences that could be recognized as "volunteer work," ( if you can't find any in your past, definitely do try and get some, and © if you don't want to gain the type of volunteer experience described earlier, you may want to look at other programs such as the MPP, MPP/MPH, MPH stand-alone, or MHA.