I feel for you -- I applied last year and had a hard time finding any concrete admission stats for sw doctoral programs. Here are a couple of nuggets, though:
Social work has some of the lowest average gre scores of any discipline. You can see here (on page 4): https://www.ets.org/s/gre/pdf/gre_guide_table4.pdf So, if your idea of competitive includes other fields, then your scores are probably even better than you think in comparison.
A lot of it depends on which schools you're applying to. Michigan, Chicago, Columbia, Washu, Upenn and any other really good programs that I'm forgetting have a lot of name recognition so tons of people apply. They usually accept somewhere between 5 and 10 people a year with more than 100 applicants. For programs like that, the acceptance rate is usually somewhere south of 10%. The same is true for programs based in urban areas (though the admission rates are likely higher) because there'll be a larger pool of applicants trying to stay home.
Which schools are you thinking of applying to? With good scores, research experience, and an advanced degree in a related field (MPH) you probably have great chances of admission at most programs (most applicants likely won't have all three of those things).