Why might it be that the lymph nodes in my neck be hurting?

Infection : Usually lymph nodes that are hurting are related to infection. Infection can be in contiguous soft tissues or even in the nodes themselves. Neck nodes often respond to infections of tonisils, throat, or pharynx. Medical treatment with appropriate antibiotics is sometimes necessary. Nodes involved with tumor often are not associated with pain.

Monitoring Centers: Lymphatic system absorbs/carries things too big to go into the arteries/veins like bacteria eaten by white cells and digested food. Lymph nodes "taste" the lymph for anything bad like bacteria/viruses/cancers, etc. When it detects a problem, it alerts the immune system and your body reacts. They enlarge in response to the inflammation they create when they react. They shrink when all is well.