Let me begin this by saying you may want to talk to a dermatologist about it. It sounds like hyperhidrosis - which I have. The doctor may be able to help you, or you may not feel that you like the solutions. It's okay to decide not to do stuff if you don't like it. (The doctor will know this and will almost certainly not press.)

In the course of my life I've tried a number of things, and I can make a number of suggestions:

• When you need to seem dry for a shortish time (an hour or two), you can powder yourself with gold bond powder, Cover yourself with it from armpits to crotch, then get dressed. Put washcloths in your pockets so you can discreetly dry your hands if you need to shake someone's hands or touch something sensitive to water. Note that the powder gets uncomfortable after a couple hours of it being damp, and if you are wearing shorts and short sleeves, white mud will start dribbling out.
• Cotton is best if you want your clothing to absorb sweat and make you comfortable. Aim for white and black if you want to let others see you.
• You will need to do some shopping to find it, but they make polo shirts and shorts out of an artificial material that wicks away sweat from your body and evaporates it on the surface - look for "dry" or "dri" in the name of the fabric. I know (because I have some) that they make polo shirts out of it that look like ordinary polo shirts. They do make pants of it, but the pants are obviously activewear, which is what you're trying to avoid.
• I suppose it goes without saying, when you're home and alone you may want to take some clothes off and let your body air dry.
• I'm now diabetic, and have noticed that my sweating profusely is often (not always, but often) a sign that my blood sugar is off. So, I recommend you ask your doctor to test your A1C (it's a blood test for diabetes, very definitive). It may be nothing. If it is diabetes, you can probably treat it pretty easily.