No, there is not more than one type of rain rot. Rain rot is an infection by a specific type of bacteria which causes the formation of scabs and hair loss in the area where it is affecting the skin. If there aren't scabs, it's not rain rot because the bacteria causes scab formation to protect itself from the oxygen rich atmosphere outside the scab. Baby oil is a poor choice for treating rain rot because it actually will protect the bacteria by keeping oxygen out as well.
For dry skin, consider that it's a dietary imbalance that is causing the problem--remember all parts of the body work together and the diet affects every single part of the body. Check the diet and ensure that it's balanced. Then consider adding a bit of oil to the diet to help heal the skin from the inside out rather than using baby oil.
Licensed Veterinary Technician