。
I couldn't say a word, choked up with tears.
Literal
Tears [with-に] choked, anything [object-を] could-not-say.
むせぶ ('to sob, choke with emotion, weep uncontrollably') is a literary verb. 涙にむせぶ ('to be choked by tears') is a standard set collocation. 何も言えない ('can't say anything') uses the 何も + negative pattern, where 何も pairs with a negative predicate to mean 'nothing.'