Please continue with the medications advised by your Doctor.
In kids with runny nose - due to frequent and rough wiping of the nose, small ulcers can happen inside the nose. Since nasal mucosa is supplied with lot of blood capillaries- even tiny ulcers can bleed for sometime.
It may recur again if wiped roughly.
Such nose bleeds are common in winter season especially when dry air blowers are used.
Be sure that room air is not dry. While wiping his nose, be gentle.
You may use nasal decongestant sprays- after getting it prescribed by your Doctor.
You may use it SOS when its too much of a runny nose.
Do not make him blow the nose- as it will end up in middle ear too.
might take 4 to 5 days. Cough
might take 1 to 2 weeks to get okay.
You may get Medications like Benadryl
prescribed by your doctor for cough and cold.
Give him plenty of fluids.
Hope my answer helps you.
Wish your son a speedy recovery.