Congratulations on taking the plunge to train for your first tri!

Well, I would like to see the training plan to give solid advice... but I strongly suggest that you GET IN THE POOL ASAP!

This is where most people need the most work. It won't hurt one bit to start now.

As for the running... you can start a run/walk plan right now as well. Slowly up your miles every 2-3 weeks until your training plan starts.

Good luck with training!