Let's have a look at what IUPAC say; they would be a reliable source to get definitions of chemical terminology from:
Monomer:
"A substance composed of monomer molecules."
Monomer molecules:
"A molecule which can undergo polymerization thereby contributing
constitutional units to the essential structure of a macromolecule. "
Polymer:
"A substance composed of macromolecules."
Macromolecule:
"A molecule of high relative molecular mass, the structure of which
essentially comprises the multiple repetition of units derived,
actually or conceptually, from molecules of low relative molecular
mass. "
These definitions are consistent with the latest IUPAC Compendium of Polymer Terminology and Nomenclature, IUPAC Recommendations 2008
Note that, historically, the definition of a polymer has changed somewhat. Up until about 80 years ago, polymers were seen as molecules comprised of similar empirical formula - benzene, for example, was considered a polymer of acetylene. It was Staudinger's work in the 1920's (contributing to his Nobel Prize) that defined polymers as macromolecules.