I am indispensable to you. (Right?)

[mlund]

Jealousy sits like heartbreak in my bonesThroughout the poem you talk about how they are still yours and pleading them not to leave, so if they haven't left how can you have heartbreak? Maybe make that idea more clear
The same hollow cold
The same sour ache
The same desperation
when you can't let go
but your heartstrings are yanked so hard they might break. The use of the word "heart" again in this line is too much. Try using  different metaphor.

Jealousy doesn't eat me up inside,
jealousy twines into my veins like vines,
jealousy is mine, jealousy won't leave me
don't you dare leave me
all you need is me
(let's be real, you don't need me)

Jealousy seeps into my skin like fear:
pricked ears, verge of tears,
looking over my shoulder to see if you're near
(stay here) By saying you are looking for them implies that they are not there, so how can you tell them to stay?

Jealousy is me begging you please on the inside
Don't forget me, don't leave, what would I do otherwise?
They mean more to you than I do, but I mean something, right?What do you mean by "they" who is "they"?
We have something special, you'd never leave me behind.

Right?

I love your use of triplets throughout the poem; you do a really good job of continuing that structure which results in a really nice flow. However, I am confused by your change in rhyme scheme throughout (sometimes you rhyme and sometimes you don't); perhaps stay a little more consistent with that.

The title really pulls the whole poem together, as it alludes to the final line and integrates with the entire theme.