Schadenfreude is "enjoyment obtained from the trouble of others." I'm not looking for the antonym of that, but instead if there is a similar word for the object of schadenfreude. For instance, is there a word for me knowing (or being troubled that) others are experiencing schadenfreude at my expense?
'Schadenfreude' is a German word. 'Opfer' i.e. victim, describes the person suffering from schadenfreude.
The concept of self-pity encompasses negative feelings by the suffering person, but it primarily concerns the source of the pain, rather than additional pain based on others' enjoyment. Cambridge defines it as
care and sadness about your own problems
At times, those who are identified as self-pitying are even thought to take some satisfaction in their suffering. American Heritage defines it as
Pity for oneself, especially exaggerated or self-indulgent pity.
Martyrdom is similarly used to refer to those who suffer and perhaps derive some self aggrandizement in their suffering. Compact OED offers, as one definition of martyr
a person who displays or exaggerates their discomfort or distress in order to obtain sympathy
Again, the word does not generally convey an enhanced pain based on others' joy.
Riffing off @WolfSchumacher’s answer, you’re after a fear (Angst) of being the victim (Opfer) of schadenfreude (Schadenfreude). German being famous for its compounds, you could coin:
It’s preposterous, but Schadenopfer (victim of damages), Opferangst (fear of victimhood) and Freudenangst (fear of joy) are all attested to varying degrees.
The resulting term would, of course, be entirely incomprehensible to English speakers, however. An all-Greek offering isn’t much better epicaricacothymophobia (working off mac389’s comment). And maximizing parts familiar to English speakers hardly improves things: I don’t see schadenfreudothymophobia taking off any time soon.