How do I train for a 5K race in three weeks?

On March 21, I will be running in the Great Human Race. It is sponsored by the Volunteer Center of Durham, and all of the volunteers of local organizations will be lining up to race for our causes. As expected, I am racing for my animal rescue group, Independent Animal Rescue (IAR).

I will be competing in the women’s 20–24 bracket.

I have a fit body, but not a lot of stamina. Currently, I can only run about 2 miles straight. (5 kilometers = 3.1 miles.) Will I be able to run for the full 5K in three weeks if I train everyday? If so, what is the best way to go about training?

Should I focus on speed or stamina?
How much is it healthy to push myself beyond my current limit?

Fitness experts and runners, please offer your advice! I am devoted to running as well as I can to support the animals of Durham!

P.S. – If you are so kind as to be interested in sponsoring me, please feel free to read more about my cause and support me here. Even the smallest donation brings me closer to my personal fundraising goal of $1,000 and to the overall IAR goal of $12,000.