Dear G.,
Hair color is safe. Perming is safe. And straightening your hair is just about the same as making it curly, only with the opposite result intended.
Make sure you have a well vented area and don't get the chemicals on your hands and skin. It won't hurt your breastmilk.
That said, if you have naturally curly hair, why would you want to straighten it? Especially if you are used to putting it in a pony tail and going to work with it still wet? I have straight hair, and believe me, there is no way I could get away with just throwing in a pony tail and going off to work with wet hair. Thinking you can just leave it down, straight and wet, is even worse.
You can do what you want and I certainly think it's high time you go to a salon to treat yourself. But consider getting a good haircut that will allow you to get out of the shower, put a little product in your hair, and embrace your curls. It can be dry by the time you get to work, or shortly thereafter, and you will have volume and body and shape that straightening your hair will not allow you without having to work and work at it. And it sounds like you don't have the time.
I know, personally, I would give anything not to have to put some shape INTO my hair.
See a good hair stylist and best of luck!