Our new little Milli is sick for the first time today

I took her on her first " in the bag" trip to the store, and on our way out, she threw up. Then in the care on the way home, she had diarrhea
So we're all cleaned up, car's febreezed, and she's had a bath. She's 16 weeks and 3 lbs, but I rubbed some Karo on her gums just to be safe, and we've been giving her water.
I'm not sure if this is from the car ride, being bounced around in her bag, her being cold or scared, OR, if it's from the plastic toy I found that someone chewed a chunk off of. My hubby said not to worry, we'll just watch them to make sure they both eat and poo, and the plastic should pass. Emma's eaten parts of toys before and they've come out, so I'm trying not to freak out too much.
I posted in the health and diet section on how to prepare the chicken and rice for dinner-is there anything else I should do for a younger puppy with vomiting/diarrhea?
Thanks!