Thanks for using Health Care Magic.
Read your query.
Swelling and rotten teeth as you have described in your query suggests 
abscess in relation to the decayed teeth. All teeth decayed will not necessarily go for extraction, only after you get it checked you can have a idea on the treatment plan to be undergone.
I would advice you to take your brother to the 
dentist for a check up and get the decayed teeth filled or have 
root canal treatment done after having an radiograph done.
For the pain , he can have 
ibuprofen ( if he is not allergic to any medicines) and may also require antibiotics like 
amoxicillin after prescription from dentist.
As there are decayed teeth ,leading to inability to eat properly will also effect his food habits and will cause related digestive problems 
Do not apply hot bag externally.
Hope this was helpful.
Thanks and regards.