Answer : No es grammatically correct in Spanish.
Explanation : The subject in these sentences was "el brazo" or "la pierna". But when applying the possessive adjective "Mi", this determinant replaces the definite article, which is now unnecessary. The correct sentences are : Mi brazo está roto. Mi pierna está rota.
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]