I recommend that you go to see your primary care doctor
about this issue as soon as possible. This symptom is potentially concerning and should be checked out right away.
Although you are right that swelling in the side of the neck is generally caused by swollen lymph nodes (glands), it is unusual to have the entire side of the neck swell. However, in more severe cases, multiple lymph nodes might be involved and could give this appearance. Generally, the swollen area should be tender if you touch it if this is swollen lymph nodes. Extensive lymph node swelling is often a sign of a serious infection, which is why it needs to be checked by your doctor.
Your doctor will also consider the possibility of an in infection under the skin could lead to an abscess
, or build up of pus, which could also lead to swelling of the neck and which, generally, would require draining of the abscess to heal up.
In the meantime, if you have any urgent symptoms, such as high fevers, difficulty swallowing or breathing, or difficulty moving the neck, you should not wait to see your primary care doctor but should instead go right away to an emergency room for a more urgent evaluation.