Hello dear,
The nose bleed can be either due to a fracture of the bony plate at skull base or due to injury to nose.
Though initial check up by the medics have ruled out possibility of
concussion, it will be better to get an X ray done to detect any injury to skull base and nose.
Regarding the goose egg on forehead, it is due to accumulation of fluid & blood and it is called Hematoma.
The blood cells accumulated are eventually broken down and absorbed in the body.
But this is a slow process & takes times to disappear completely.
Till that time, symptomatic relief is obtained by analgesics preparations (like paracetamol/
ibuprofen)+
serratiopeptidase, ice compression & adequate rest.
If it still persists or there are any other associated symptoms like fever, vomiting,
dizziness,
loss of consciousness, convulsions, etc...then it will be better to consult a Doctor.
Till then, maintain adequate hydration & nutrition status.
There is no need to worry, he will be fine.
Wishing a good health.
Take care.