"I can run a finger on my arm pits and feel slipery/greasy residue that I had scrubbed off only seconds earlier." I could be wrong of course, but can't help but think that this is nothing but residual soap compounds soaked into the skin (normal, don't worry about it...simply rinse thoroughly) or soft water (which sometimes feels "slimy"...? Bodily sweat is a combination of water, salts, oils, and whatever else (including toxins) that might be released into the pores via the bloodstream. I can't possibly see that stuff substantially building up just seconds after a lather and rinse.
If you're not already doing so, use a deodorant soap since these contain antibacterials such as triclosan or similar. I once read that shampoo has a stronger antibacterial action than common (non-deodorant) hand soap, so that's an option too, but I'd simply go with deodorant soap.
You mention using an antiperspirant. These have aluminum-based or other pore-clogging compounds. Instead, you might try a deodorant stick since these don't stop perspiration but do contain antibacterials, typically triclosan. Some deodorants use alternate compounds which I can't recall -- if you can find British Sterling deodorant (sold in the U.S.), it contains an alternate antibacterial instead of triclosan (read its label). You can find a women's equivalent using that same chemical and try that as well as triclosan. Salt crystals (big chunks of salt, I think) have also been used by some folks on the underarm, although I don't know their effectiveness -- you can easily find these on the internet. You might also look into the "natural" deodorants such as whatever's carried in the "Tom's" line of natural products. "Tussy," sold in drug stores the U.S., is a heavy cream deodorant. I'd guess it may be quite effective since it's so thick and heavy an application that should last through the day.
You mentioned a skin yeast infection and constipation...you should take the following candida questionnaire (first link), although your situation may have nothing to do with candida. Should it suggest you have candida, go to the second link:
Increasing your fiber content, drinking plenty of water/liquids, using over-the-counter remedies (Metamucil, etc.), and the herbs buckthorn, cascara sagrada, fenugreek, senna, and vervain all have well-known laxative effects. Good luck!