Do I have a chance of getting into a good mechanical engineering grad program with a low gpa and a degree in Biology?

Hi! My goal is to get my MS in mechanical engineering but I’m not sure I even have a chance of getting in.. I graduated with a BA in Biology with a minor in Chem but with a 3.05 which I know is not good. Since graduating, I’ve taken Microbiology and Calc 1 and 2. I received an A- in microbiology, an A in calc 1, and a B+ in Calc 2. I plan on taking Calc 3 and hopefully discrete as well. I did research for about 2 years, working with a virus and am about to publish a manuscript on it. I currently work at a biotech company and have had the opportunity to shadow some of the engineers here which is what made me want to do engineering. I’m wanting to apply to schools in the south, but my dream school is Vanderbilt (which I know is probably a huge reach). Any advice would be greatly appreciated.