Grammatically, 押し戻してなかったことにしたい can be both the contraction of 押し戻していなかったことにしたい, as zuotengdazuo-san interpreted, and 押し戻して、なかったことにしたい, as Chris-san did. (More accurately, it's "I pushed the tears back in and I wanted to pretend they had never been", though.) Judging from the context, Chris-san's interpretation is correct in the example sentence. "I want to pretend I haven't been shoving the tears back" is not the same as "I want to pretend I'm not shedding tears" in meaning, and the latter is his intention here.
涙なんか is the object of 押し戻す, and at the same time it's the object or subject of なかったことにしたい. (Both 涙を「なかったこと」にしたい and 「涙がなかった」ことにしたい are possible. The meaning is the same anyway, though.)