First of all, all you can do is apply, and as Walter said, you may be able to ask through informal channels what your chances are.
Second, it may depend on the program you're applying to, and how holistic their application evaluation process is.
Finally, really do consider whether going right into a Ph.D. program is the right choice for you.
I understand your lower grades are partially (or even mostly) due to external influences (believe me, I understand), and grades don't reflect the whole student, but they are one indication. Your grief about your mother will likely continue to complicate matters, so how are you doing in that area? How raw is it for you still? Under objective scrutiny, are your focus, decision-making, and emotional stability representative of the you that you want to expose to the rigors of a Ph.D. program? Or should you give yourself a little more space before you start?
Another question in this area is, are your low grades indicative at all that, maybe, you have a passion for public health but possibly not in this field? What changes do you want to effect in public health, and is your current field where that work happens or is it actually another field? (An extreme example would be if you're really more interested in public health policy where a law background would serve you better or public health infrastructure where you actually need engineering, or something along those lines.)
And I'm sure you've exhausted this question there and back again, but is this the right program for you? Of course, the right program is not the best one but rather the one that is in line with where you want to go. I can't say one way or the other about your grades, but you should at least be applying to a program that has a focus on public health and especially one that values your passion, even if they can't admit you in your current situation.
Just remember that a Ph.D. is an extraordinarily demanding thing, and that there are definitely people who regret the experience. If it is going to be a positive and productive step in your life and career, you need to be solid on the reasons you're there. It's especially worth evaluating a little extra if you're motivated at all by momentum, like if you stop, you won't be able to restart.
I may be completely off-base with my advice. I just had to say it just in case you're like me, because so much of what you describe is exactly where I was earlier in my life. Ultimately, if you want to apply, apply. If you're on the fence, explore your other options and then make your decision. There are likely many more than you imagine. And if you're just waiting on tenterhooks to hear back, best of luck!