Living in a places with weather very similar to what you describe (Raleigh, and before that in south Florida, Orlando and Tallahassee), I used to feel the same. I hated walking anywhere outside. I recently moved to a walkable neighborhood and since I'm motivated to walk and bike more since it's easier than driving, I discovered that despite thinking I was dressing to be comfortable in hot + humid weather (shorts and a t shirt), I wasn't. I was dressing to be comfortable once I finally got out of the weather (pretty much exclusively in air conditioned buildings). As a result I was spending as little time as possible outside, which reinforced the way I was preparing for the day.

I've only really made a few changes so far (breathable/better ventilated shirts and shoes, and not wearing socks when I can do without). It's still hot and I still sweat, but much less and when I do sweat it evaporates more easily and I feel cooler. I also now try to bring a sweater if I'm going to be inside for hours, just in case they have the AC really cranked (occasionally I'll find it's needed at work or in movie theaters).

I guess it's not really a great solution if you are restricted in what you can wear to work though. There are supposed to be breathable suit fabrics (like linen) that are good for hot + humid weather, but I have tried them. I wonder if we'll see increasing acceptance of "professional summer workwear" in the US as the sunbelt continues to boom. Maybe that's part of the reason athleisure has become so popular?