Brewhaha

I need some advice. I have a degree in graphic design and I'm interested in becoming a product designer. I'm 33 and I'm looking into grad schools. 1)Do you think it's necessary do go to school to become a product designer or just have a great portfolio? I have great drawing skills - 2)Are there grad schools that teach product design or do you think I'll need to get another undergrad degree in product design? - That is, to get hired as product designer. 3) What's the entry level job title? What are the entry level jobs you look for? Thanks in advance!