What are the hard lumps on the back of a 3-year-old's upper neck and lower head area?

Answer

Are you mad? They could be anything, take the child to a doctor.

Without examining this child, I'd have to "guess" (which does NOT take the place of a physician) that the child has a long history of ear infections... and that these are lymph nodes...

As I answered in another question, lymph glands filter out the "poisons" from infections and viruses throughout the body... They also are a part of the body's immune system.

The cells of the lymph glands (nodes) actually grow in order to filter (neutralize) poisons from infections... then after the event is taken care of, shrink back down... but because they are "scarred" from handling their job they don't shrink back down to their original size... You then have these small hard knots left over... I'm in my late 60's now, and still have remnants of these lymph nodes palpable in my neck.

Smart thing though would be to get someone to examine this child...

Oh... The nodes in the back of the neck & at the hair line are called the "posterior chain" of lymph nodes and normally are the ones that become enlarged dueto a history of repeated ear infections...