Can understand your concern..
As your son is diagnosed with tonsillitis
, it is most commonly due to bacterial infection, so medicines given to him are appropriate if given in paediatric doses..
As a matter of concern about blood in phlegm, as your son is having excessive coughing it may be due to inflamed tonsils getting trauma due to which there may be rupture of some micro bleeders causing slight bleeding appearing in phlegm..
If the blood in phlegm is persistent and the condition is not improving you should see a doctor immediately..
Throat swabs for culture and sensitivity can be taken to find out if the infection is bacterial or viral in origin..
Blood analysis: CBC ,ESR
These will help to find the exact cause of his illness if the above treatments does not work and no recovery is apparent.
By the time continue medication and give him soft diet
Hot milk with pinch of turmeric bedtime can be relieving as it has antiseptic properties.
Warm saline gargles should be done..
Keep him well hydrated to prevent dehydration
Hope he gets well soon..
Thanks and regards..
Dr.Honey Nandwani Arora.