Fallout from the bombs isn't the only form of Radiation, and your comparing the West Coast to East Coast, East Coast got the Blunt of the Strike.
The East Coast didn't get the blunt of it. DC is still standing and so is Pittsburgh, the only two cities we have seen on the East Coast. Yet L.A, San Fracisco, Bakersfield, and many more in California have been completely wiped off the map. Only looted heavily damaged burned out building still stand in some areas.
This idea that the "East got it worse" is a totally fan maded explanation supported by nothing. Bethesda admitted they didn't want DC to be realistic, as in look the way it should after a nuclear war. They designed it the way they did because they thought it would be fun and cool.
Radiation does come from other sources I will give you that. Like The Glow in Fallout, Gecko in Fallout 2 and Vault 87 in Fallout 3 and Vault 34 in New Vegas. But radiation doesn't stop plant life from growing. There should be plant life in Fallout 3 and yet there isn't while in all the other games there is. And I am not counting Oasis and later point lookout. Vault 87 wasn't explained as to why everything is irradiated in Fallout 3.