My puppy hasn't eaten in 2 day and hasn't pooped in 2 days

You should try different food and the reason it hasn't pooped is because it hasn't eaten if all fails take your puppy to the vet

2 days is a long time for a puppy to go with out food. Is he drinking water and staying hydrated? It could be anything from worms to a blockage, you really should take him into the vet.

What's wrong with my puppy, he drinks heaps and eat occasionally but then ends up either pooing it all out or vomitting it up

Has your puppy been dewormed and vaccinated?
Is the poo bloody or watery?
How old is he?
How does he act otherwise?
It could be worms, a gastric upset, parvo or any number of things.
Puppies can go downhill pretty quickly when they get sick.
A visit to the Veterinarian is what I would suggest

My puppy hasn't eaten anything for the past 2 days, what could be his problem. It's raining could that cause him to get sick, and can he die?