Disclaimer: I am NOT a doctor -- if you have any questions about your own health, seek professional advice. This is just my personal experience.
I think the sweats can come when you start realizing you are getting sick -- adrenaline kicks in -- Oh no, I'm getting sick! I panic, I sweat.
BUT, I also think it could be a sign of something else. Dizzy AND sweaty is usually a sign I need to eat. No fanny pack is complete without a trial size deodorant and lots of antibacterial wipes for cooling off.
I started off with ear infections that wouldn't go away. When they finally did, I was still dizzy. GP sent me to an ENT who sent me to a neurologist who put me on meclizine (prescription strength -- couldn't hack it so now I take over the counter and HALF the pill so I can still function -- so much for non-drowsy for this lightweight). I used to have severe migraines also -- often while driving. Meclizine was wonderful! My lil yellow happy pill took the edge off everything (even the headaches), curbed my appetite (lost weight!) and also helped with my allergies since it includes an antihistamine (which is what curbed my appetite). The only problem -- I couldn't hold a thought because I was so sluggish.
To make a long story longer (sorry!), I _finally_ found out most everything went back to low blood sugar, hypoglycemia, for me. Even though I test in the "normal" range for blood sugar, I get low easily between meals or if I eat the wrong foods. This is sort of the opposite of diabetes, but the recommended diet is very similar. I don't need medicine for it. I might need meclizine 2x a year now to control dizziness. I just eat more often and try to avoid sugars and simple carbohydrates (well--at least only in moderation and preferably with protein). I rarely get a headache either.
BEFORE:
When I am at WDW, I am in sensory overload. It can be easy to "forget" to eat or stick to a normal schedule. Breakfast might be a nutrigrain bar and OJ (sounds "healthy," but too much sugar for me by itself). I need a quick bite around 10:30 so I reach for a coke and candy bar (NONONO!). By lunch, I am irritable -- not mean, just _easily_ annoyed -- and my head has started hurting. Grabbing a quick bite doesn't seem to help -- so I have to sit down by 1:30. If I don't eat something good soon, I will be out of commission for the day. Well, meclizine helped ease the headaches and the dizziness -- but since it curbed my appetite if I took it regularly -- it actually hurt me. I didn't want to look at food, and food was the only thing that made me feel better.
NOW:
I do great now that my husband and I know what to look for. Do you feel fuzzy -- hard to concentrate? Do you get the shakes? Are you sweaty when you aren't really hot? Are you lightheaded? Do you feel like you are spinning? I also have clued in that if I keep dropping things, I probably have shakes in my hands and don't even realize it. DH keeps me to a strict eating schedule -- breakfast (preferably with eggs involved), something light at 10:30 or so, lunch, mid-afternoon snack (not too sweet), early dinner, light snack if I need it around 8 or so. It makes all the difference. I can ride most rides -- but this last week, RnR did get me. I sat down for 10 minutes while DH ran over to ToT and was fine the rest of the day. I don't do ToT -- too chicken. Star Tours got to me a lil this time, too, so I just focused on the droid instead of the flashing lights. Eat before you ride! I know you think you will be more likely to get sick, but you might find the right food will actually settle your stomach. Peanut butter and jelly sandwiches are wonderful pickmeups if you feel "low." PB&J are often on the kids' menu.
EAT!! Eat healthy and often. Stay hydrated (water not soft drinks -- be careful of too much juice -- it is high in sugar even though it is very good for you). Take it easy. Split a child's hot dog meal with someone and see if you feel better even if you just ate an hour ago. Keep the Mickey Bars to a minimum. Try it at home. See if it helps. It has made all the difference for me.
Good luck!!