'Was' is the linking verb, 'Swollen' is an adjective. 'With melted snow' is an adverb. That's how I see it.
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bmojtaba*The river was swollen with melted snow.*You can say: " The river is swelling with the snow runoff". You can also use "cresting" and "swollen" to describe a river which is rising rapidly. Each word projects a slight different meaning however.