It depends a little bit on your context... since tear has two different pronunciations and meanings.
Most of the time, this phrase will be the verb form:
(v) to tear something up / to tear up something : means to rip something apart (like paper)
This is a proper verb: tear (present), tore (past), torn (past participle)
'it tears me up' (inside) : it's very painful/saddening. Imagine that someone has taken your heart and ripped it up like a piece of paper. It makes your chest feel tight and uncomfortable like you want to cry.
Sometimes (not as commonly and always informally): someone may use the noun pronunciation /tIər/ instead of /tɛər/
to tear up: to make your eyes water, to begin to cry
This is almost only used when talking about yourself; 'I teared up', 'Don't make me tear up', Cutting onions always make me tear up.
Because this is not using the actual 'verb' tear, we just add 'ed' for the past
tear up, teared up, teared up