I am looking for an adjective that describes a person who doesn't want any sympathy or empathy for himself/herself.
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You could say someone is "too proud" or "too stubborn" to accept sympathy.
They could be "abrupt" or "abrasive". Maybe "standoffish".
"Independent" could also be used for a positive spin.
self-reliant free dictionary
Reliance on one's own capabilities, judgment, or resources; independence.
A 'stoic' is someone who does not seek sympathy. 'Stoic' is also the adjective so can be used descriptively.
If you say that someone is a stoic, you approve of them because they do not complain or show they are upset in bad situations.
One who practises repression of emotion, indifference to pleasure or pain, and patient endurance.
Bit-by-bit the stoic, infallible image of sporting heroes is turning
I suppose you could say antipathetic, but I think that is just a general distaste and aversion to something.