Will my poor performance during my masters degree make it impossible to get into med school?

So I've been seriously thinking about apply to med school in the future. I would be a non traditional student, my BA was in psychology. I was working as a research coordinator for a number of years before I decided to get a MS in statistics, unfortunately I just happened to pursue this degree in the worse time in my life. My first semester, right before midterms someone extremely important to me died unexpectedly to cancer that we were not aware she had. I then suffered major health issues for the remainder of the degree. My GPA is at a depressing 3.48.

I would love to pursue a degree in medicine, I would have to take two years to complete all the prerequisite courses and obtain clinical hours. I have been working in research a long time so I course have loads of hours, my research position had me doing a lot of diverse task that involved a lot of community outreach. I have 6 publications, with 3 in progress, and 6 poster presentations.

I adore research and would love to get into the research focused top 20 university (also this university tends to cover more of their students tuition, their students graduate with less debt which is appealing to me) near me but if that's impossible, which is might be given my MS performance, there are other medical schools with great programs near me, one of which is the very university that I've worked for for 5 years. I have a 3.98 GPA in my BA and am confident that I can get As in all my pre-med coursework. I feel I can be an excellent writer and have been told several times that I produce amazing personal statements. I obviously can't attest to my MCAT scores yet, but what do yall think? Have I completely screwed up my chances to get into any med school much less the more prestigious ones?