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Your cheapest and easiest thing to do at this point is to take in the diarrhea to your vet and see if you have coccidia. If positive then you need to pick up the medication. If they don't see anything on the fecal...you probably need to consider bringing the puppy to the vet because of the age...they get dehydrated quickly.
The vet can give an injection to slow down the vomiting.
let me know if you have further questions.