Hard lump on my head, been there for a month, skin moves freely over it, about the size of a v.small grape. no pain, not tender, unmovable.

Likely a lymph node: There are a number of lymph nodes scattered around the back of the head and neck where they are easily found. At rest they may be the size of a pea and when stimulated they are often bean sized or larger.Size often changes over weeks ; often reflects bug bits, skin rashes or throat irritation, it is not likely related to headaches, nausea or dizziness. Your doc can confirm this.