The bad news is that it is an illness - but it's also a common problem, known as hyperhidrosis.
You're sweating so much because your sweat glands are functioning non-stop at full-capacity!
How do I fight hyperhidrosis?
The first step is to visit your GP. They see this type of thing all the time so don't be scared of telling them the full extent of the problem.
Your doc may prescribe specialist deodorants - just be careful to pay attention to the instructions for usage.
Alternatively you could be referred to meet with a dermatologist who can diagnose illnesses such as hyperhydrosis, bromohydrosis, or prickly heat...But don't panic, they're easily cured!
One of the most common treatments is to apply an aluminum solution followed by a polyethylene film that you leave on overnight. The next morning you take off the film, take a shower and wash with an anti-septic soap with anti-bacterial properties.
You can also investigate botox as a potential treatment for excessive sweating. It's proven to be very effective and can sometimes be prescribed on the NHS. More often though it's carried out as a private procedure. Prices start at £150.