I grit my teeth and force down the emotion that had risen to my throat.

Literal

Teeth [object-を] clench-bite, throat-base [up-to-まで] welled-up-[past-た] emotion [object-を] forcibly swallow-down.

Narrative prose depicting intense emotional suppression. 歯を食い縛る ('to clench-bite the teeth') is a set phrase for gritting one's teeth against pain or emotion. せり上がる ('to well up, to rise') is a compound verb 競る ('to press up') + 上がる ('rise'). 喉元 ('base of the throat, the hollow above the chest') is where rising emotion is felt physically. 強引に ('forcibly, by force') is the adverbial of the na-adjective 強引.