Well, the first thing is that white females make up an absolute majority of the class at some law schools now, so you're neither a minority nor under-represented (URM applies only to racial minorities with chronically low rates of enrollment in higher education). Also, at 22 you are not a non-trad (most people think of non-traditional as meaning students who have significant work experience after college and start law school around age 30 or later). Most 1Ls don't have children, but parents are not a class that gets any special attention in higher education admissions.
With the right numbers, being a single mom will not keep you out of any law school -- but it won't get you in either. It does work well in an academic addendum if you need to explain any blemishes on your transcript (but it works even better if you did well despite having the added work of being a parent and supporting a child). If you write your PS on your experience as a single mom, then you have to figure out some way to make that relevant to law school -- in other words, it can't just be, "I raised a child on my own while also finishing college, and that was really hard." Not that it's not a big deal that you managed to do it, but it's just not what they're looking to learn about you. If your experience as a single mom has informed the sort of work that you want to do (family law, women's issues, child advocacy?), and if you have any sort of volunteer or work experience to go along with that idea, then it might tie in well. Schools may have concerns about how you will balance the two very heavy workloads of law school and parenting, so to that extent showing how you've learned to do that well is not a bad thing to devote a little space to in an addendum or your PS.
I haven't been paying attention enough to know if we have any single moms on here this cycle. There was one poster named caribelita last year (or the year before, maybe) who was in a similar spot and got into a great school. You might try sending her a PM to see if she's still around and has any advice.