1. gemmaphile (polite) or 2. Jewel-junkie (impolite)
gem derives from the Latin gemma according to Etymoline
a precious stone" (especially when cut or polished), c. 1300, probably
from Old French gemme (12c.), from Latin gemma "precious stone,
phile as we all know derives from the Greek philos, loving (See dictionary.com)
But this combines a Latin root with a Greek root, which I once read is not quite proper. However, Wikipedia on Hybrid Word gives many examples, e.g., automobile and bigamy.
- The impolite word, jewel-junkie
Jewel does not need to be defined. Junkie, as defined by Dictionary.com
a person with an insatiable craving for something: a chocolate junkie
a person who gets an unusual amount of pleasure from or has an unusual
amount of interest in something: television news junkie
The first definition of junkie is "drug addict", but the second definition in these and several other references is to a legal, even innocent, craving.
Jewel-junkie would be OK in the US, if said in an affectionate way, but might be over the line somewhere else.