Your adenoids are not really in your nose. They are usually in the upper part of the throat, directly behind the nasal passages. You can usually see them in babies but as we grow older they shrink. But in some people they do not shrink and instead the adenoid tissue actually get bigger. It is this large tissue growth that people call the adenoids. If this adenoid tissue gets repeated infections your doctor will recommend getting removing the tissue surgically.
You can try to build your immune system to fight infections by taking supplements such as probiotics and echinacea. Honey is also a natural antibiotic.