I was in a similar situation to yours. I was in my junior year when I told my advisor that I wanted to go to dental school. She looked at my GPA, similar to yours, and told me I wasn't competitive enough. Skip to now having my degree, I'm working with just over a 3.65 s/oGPA, good DAT, and the same counselor told me yesterday that she is confident I will get in somewhere. Here's what I'll tell you: it's absolutely possible to turn things around.
Find out better study strategies, make the sacrifices, and talk to your professors. In terms of the DAT, your best option in terms of timing would be to use this summer to study. Sift through SDN for study resources, I recommend DAT and Math Destroyer, Bootcamp, and Cliffs AP Bio. Be prepared to devote a lot of study time this summer.
I think one of the biggest hurdles we have to overcome is finding out what works best for ourselves as individuals. Keep trying different study habits and build upon the good ones. It's going to take hard work, but that's what makes it so special. One day it'll turn into a gift that you've developed and can use to help other people!
Good luck Underdog!(;