The article I linked discusses the National Vaccine Injury Compensation Program at length. Would you care to discuss the claim in the article that this program has paid very few claims in the decades since it was created? I checked: it is the exact program created by the National Childhood Vaccine Injury Act of 1986. We're talking about the same thing.

tl;dr: the pharma companies don't have to pay you and the government is extremely unlikely to.