歯がひどく痛むんです。

tooth

indicates sentence subject (occasionally object); indicates possessive (esp. in literary expressions); but; however; still; and

cruel; heartless; hard; harsh; severe; violent; intense; strong; heavy; extreme; very bad; terrible; awful; excessive; exorbitant; unreasonable; outrageous; unfair; unjust

to hurt; to feel a pain; to be injured; to be spoiled (e.g. food)

yes; yeah; uh huh; negative verb ending used in informal speech (abbr. of negative verb ending "nu"); abbr. of particle "no"; abbr. of particle "ni" (used especially when it precedes the verb "naru")

be; is