Hi thanks for your question.
Tonsils and adenoids
are part of lymphatic system
of body and provide immunity against infection.Yes they trap and kill airborne infection.
Most probably your suffering from pharyngitis(infection of throat) and rhinitis(infection of nose) leading to congestion of nose and hypertrophied turbinates(small spong bone in nose) can block airflow during inspiration(taking air in) and cause difficulty in breathing.
Along with pharyngitis your upper respiratory tract
is also involved.
I would suggest you to consult a physician who will examine you and may prescribe appropriate treatment.You may need a course of antibiotic,antihistiminics and nasal decongestant
Hope this answers your question.