Antiperspirant is not a solution, it only covers the issue. It would be good to control underarm odor from sweat glands and prevent sweating by controlling body temperature. The best way to do this is to work on your diet regimen so that you consume less carbohydrates and excess fatty foods which will increase blood sugar levels in the body. You can also eat more of green leafy vegetables, nuts, seeds and whole grains which have been known for its anti-inflammatory properties as well as other nutrients such as fiber, vitamins A, C & E etc., all of which help reduce sweating.
For those who are unable to follow such diet plan because they suffer from diabetes or high cholesterol or obesity then use natural deodorants like essential oils like tea tree oil (Melaleuca), neem oil (Azadirachta indica) and camomile oil (mugwort). These ingredients may not give long term relief but provide immediate relief at least for few hours.