Running is definitely better for you than drinking, assuming it's not to the extreme of causing physical harm. Perhaps you could find a trainer or someone else who has experience with triathlons locally and plan out a healthy/reasonable training plan for the months/days/weeks leading up to the race.
I used to run a lot in my younger days. Not sure how much training you've had, but have you ever run a half-marathon before? ( 13.1 miles ). If not maybe a 5k or 10k would be a better place to start.