Over many years of fielding this basic question, “I have a _____ degree and I want to be a designer, should I get a Masters in Design?” the majority of the recommendation has been that if you really want to do be an Industrial Designer you should most likely pursue an undergraduate degree in Industrial Design. Undergraduate programs give you the time to develop your sketching, form giving, modeling, and technical skills while you are learning the design process. Masters programs are generally much more focused on specifics and shorter in duration leaving less time to develop the core skills which ultimately serve as your foundation. Unlike many professions, Masters degrees in ID aren’t hugely valued outside of Academia or more research-centric areas, so while it may seem like a step backward to pursue a second undergraduate degree very few in the ID community will see it that way.
If you are interested in Product Development more broadly, my wife currently works as a manufacturing engineer and has worked as a product engineer though her degree is in Biomedical Engineering (like yourself).