A Highly Unusual Biological Substance: Such as a large, decaying slime mold (like “Dog Vomit Slime Mold,” which can be dramatic but is typically not harmful) or a mass of insect larvae, but the severity of your reaction suggests something more dangerous.
Decomposing Animal Carcass: The smell fits, but the “slimy, moving, turned inside out” description is unusual and suggests advanced decomposition or scavenger activity.
Do not try to solve this yourself. The combination of the visual, the smell, and—most critically—your acute physical symptoms makes this a matter for emergency services.