Such products frequently contain fragrances. Unscented Or rub baking soda or green clay under your arms. Plain gelatin makes an excellent styling gel. Simply dissolve one teaspoon in a cup of warm water. It can be used as a liquid or chilled for a gel.
Sugar water makes a hairspray.
Salt water can also be used, but will be more drying. Baking soda, cornstarch, and arrowroot powder all make alternatives to talcum powders. If you have been using an anti- fungal powder, try using a solution of grapefruit seed extract instead. Wearing loose clothing made of natural fibers can also help. I don't know if they are free of petrochemicals.