Word for someone who pities, insults or complaints about their situation or life just to make the other person flatter them [duplicate]
The idiom for what she is doing is fishing for compliments
to try to get people to say nice things about one
So compliment fisher would be an intelligible phrasing.
There is an alternate usage of martyr that could apply.
"a person who feigns suffering to gain sympathy, help, etc" vb (tr)
(usage is facetious or derogatory)