I am a native English speaker but not a grammar expert, so I could be incorrect.
"Nothing we did" forms a noun phrase that is headed by the indefinite pronoun "nothing." Sometimes you will see a "that" as in "nothing THAT we did."
"seemed to help" follows the verb ("seemed") + infinitive ("to help") construction. "Seemed" is the past tense of the verb of perception (e.g. feel, look, etc.) "seem." Verbs of perception belong to the category of copular verb. The infinitive "to help" is functioning as a noun (a direct object of "seemed" in this example).