Breast stroke???

I don't know of any triathlons that require you to do only one stroke. Anything you can do on your own power without the use of aids to finish the swim is allowed. There may be some Tri's that do have this requirement but I have never heard of them. 

Technically, "freestyle" means you can swim any stroke you want.   Most just refer to the front crawl as freestyle.

But yes, you can breastroke.  In fact, there was an interview with the female winner of IM Cour d'Alene today, she said she did her first tri, a HIM, all breaststroke because she couldn't swim well.

Just make sure you are off to the side so you aren't kicking anyone 

First of all, welcome to the Tri-Life.
I've done 4 triathlons; 3 with open water swims and 1 indoor (interesting).  You can use any means personally possible to move yourself through the water without using any assistance.  My 1st open water swim triathlon was a 750 yard sidestroke effort.  I've been working the past 8 months on improving freestyle swimming.  I've got some books and DVD's from Total Immersion and there are some good video clips on YouTube. 

One thing that helped me was to actually slow down in the water.  Think about what your body is doing while your swimming and start adding little improvement changes one by one.  Your not going to change a swim stroke in a week, but you can get better the more you swim.  Try to get into the pool at least 2 times a week and spend a good hour working on freestyle.  I still switch between sidestroke and freestyle as I train long distance and during triathlons, but the amount of freestyle is increasing more and more. 

Very best of luck to you.  This will change your life...