whose is this shirt有语病吗

是对的。
whose在对物主代词提问时,既可以对形容词性的物主代词提问,也可以对名词性的物主代词提问。例如:
That is your watch。(形容词性的物主代词)
Whose watch is that?
These boxes are theirs。(名词性物主代词)
Whose are these boxes?