Welcome to health care magic.
The inability to extend the arm seems to be unrelated to the injury
in your hand.
Such inability to extend the arm may be related to the muscle injury during the event of trauma and can cause contractures
and prolong morbidity.
You should get reviewed by an orthopedician Physiotherapy
and painkillers can relieve your pain and ease the tension of the arm.
Delaying the treatment may affect the ultimate outcome.
I hope the advise will be helpful.