Hello and welcome to Just Answer Customer (name blocked for privacy):
Vomiting is common after coughing fits, which may indicate reflux. There are medications that can be prescribed for this and are safe for infants to take. Since you have stated that vomiting occurs even before coughing, I wouldn't believe it is acid reflux causing his symptoms.
Vomiting for a child under the age of 1 for greater than 1 day is cause for concern, especially if reflux has been ruled out, and should definitely warrant blood work to check for an underlying cause. Vomiting for a week is NOT normal by any standards and is not related to a viral infection. A child this young is at risk for dehydration, even with using pedialyte, that can occur rather quickly. You need to revisit with the childs pediatrician and demand some testing be performed or obtain a second opinion.
As for what the exact cause can be can not be obtained until blood work and/or other testing is done.
Here is a link regarding vomiting that will provide even more information than I have listed and which I believe you will find most helpful.
http://www.askdrsears.com/html/8/T083300.asp
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