Do I have PPD??

My baby is 1 month and I'm starting to feel seriously overwhelmed. I have a 5yr old, who wants my undivided attention and does his best to wake his brother up, I find my self struggling to do anything. My partner works and gets in late he does what little he can to help but 96% of the childcare falls on me. It feels like everything is falling apart, I'm late picking up and dropping my off my son to school, I'm feeding him junk food as I have no time to cook anything proper, I can't spend any quality time with my 5yr old as the baby demands all my attention. I'm feeling like a bad parent. I'm sleep deprived and frustrated. I don't remember it being so hard with my first. Do I have PPD?? Or just normal baby blues??