Based on the information provided it seems like "PNEUMONIA" ,
The throat infection
mostly weakens the immunity for a while leading to the superinfection
of other micro-organisms
Very important history information are missing, so I will just list some possibilities but can't pinpoint the cause
1) If the cough
is dry ? - If dry then its mostly a viral infection of lung and will be cleared by its own.
2) If the cough is producing sputum of different color it has some different possibilities
a) sputum/spit yellow/ greenish/brownish - its bacterial infection
b) Rusty / foul smelling - it can be an anaerobic bacterial infection
may lead to abscess
c) whitish - may be parasitic
3) If fever
with chill / only fever present?
These are important history points that will help to narrow diagnosis.
CONSULT A PHYSICIAN AND LET HIM KNOW whats going on
here is what they will do.
1) physical exam and try to listen on lungs for changes in breath sounds
2) will do sputum culture
3) some blood tests.
4) x-ray chest will be needed
5) TREATMENT- they will prescribe antibiotic what work on many types on bacterias first till the result of sputum test comes in and then will change to the specific antibiotics to cure the causative organisms,
Hope it helps.