I think you could try not using the body wash and baby oil for a few days, and see if the sweating goes away.
I'm not a doctor, but I also have problems with really sweaty feet, and other places too. You might have a condition called hyperhydrosis, basically sweating way more than most other people. You can get a diagnosis and help from a doctor. There are some prescription and non-prescription treatments to stop the sweating, even if it is not bad enough to be hyperhydrosis.
A great website that I get a lot of info from is that for the International Hyperhydrosis Society, which is at SweatHelp.org.
For smelly feet, I have used regular antiperspirant. It doesn't completely stop the sweating, but it does stop the smell. I use Secret Clinical Strength and rub it on my feet at bedtime.
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