I remember my mom telling me a long time ago that antiperspirant isn't so good for you. Sweating is natural: don't stop it. Deodorant is good: it's nice not to smell bad.
But somehow I learned only very recently that antiperspirant which contains aluminum is bad for us. According to this website (which is old - 2008) the results aren't conclusive, but the ingredient aluminum, which blocks your sweat glands is probably bad for us. It is not proven, but linked to cancer.
I learned this one night a few weeks ago from my little sister. I had antiperspirant in the bathroom (I normally wouldn't buy it, but I had a free sample, or someone gave it to me.) and I promptly threw it out (against her good judgement - her words: "good idea. except it's good to have something to replace it with."). So I needed an immediate solution, and found one online I've been using happily for the last month or so. I used this blog, which I love, to look for a recipe (but we learned that no, it doesn't eliminate the yellow armpit stains).
The recipe is equal parts (I use 1 Tbs each) of coconut oil (warm in microwave) + baking soda + corn starch. The coconut oil is just a conduit for the active ingredient: baking soda, which eliminates odors. The corn starch probably helps absorb moisture. You can add an essential oil if you like.
I made it in a little baby food jar, and I scoop it out. Not my favorite activity, but I'm still happy with my homemade deodorant. So, I'm buying a case of 10 empty deodorant sticks here. It's nearly $1/each this way. If you want one, let me know!
My daughter is one today.