What you are experiencing is something called hyperhydrosis. This is a condition in which the sweat glands in the palms of the hands, soles of the feet, armpits, and other areas are overactive. This leads to embarrassment in social situations, although it does not cause any other medical problems.
The response of the sweat glands is modulated by an individual's levels of anxiety
and stress. Therefore many people with hyperhydrosis find that regular sleep and exercise, and perhaps meditation or other stress-reducing activities, are very helpful in controlling the excess sweating.
If these methods do not work for you, then you should talk to your primary care doctor
about other options. The first option for hyperhydrosis are drying agents like aluminum chloride. This is the active ingredient in antiperspirant deodorants, but it is also available in a prescription strength lotion and is usually very effective in improving the sweating. Other treatments that are used include various anticholinergic medications that reduce sweating, although these are used only after aluminum chloride fails, as they have more side effects.
Finally, if these simple methods fail, there are more complex treatments, including the injection of botulinum toxin (Botox) into the areas of increased sweating.