Recently I got a Brazilian wax. I was not paying attention and I’m not sure if the wax lady was double dipping in the wax or not. But when I got home I developed a terrible yeast infection. What is the possibility of possible HPV contraction from contaminated wax? 

This was a no risk event for HPV and for other STIs, including HIV, even with "double dipping" which may or may not have occurred.  Brazilian wax treatments are inherently irritating and your symptoms, including a possible yeast infection is almost certainly not related to your Brazilin waxing.---