Hello and Welcome to ‘Ask A Doctor’ service.
I have reviewed your query and here is my advice.
Since the
adenoids were removed and the bleeding occurred after 2 weeks after the most probable cause of such bleeding from the nose is secondary bleeding from the wound caused by adenoid removal. This is usually mild and stops on its own.
Since there was a repeat bleed then it is more important to get an ENT
Endoscopy done so that any obvious cause other than the adenoid healing bed be confirmed and tackled say by
cauterization or so.
Continue with nasal decongestant drops, may need oral
steroids and so on as per the cause found.
Till you are cured no riding or any other strenuous exercises.
Take rest.
Keep yourself hydrated well.
Do not blow nos.
No sudden changes through different temperature zones.
Hope I have answered your query.
Let me know if I can assist you further.