My great-aunt Susan Jane Wright declared her occupation as chemist/chemistry when she arrived in Canada from the UK on at least two occasions in the 1920s. Given the family background, I'm pretty certain she wasn't university-educated, as they were firmly working-class. So what might a 'chemist' do in the 1920s?
Chemist is one of those occupations that has several meanings, each of which brings another web of meanings and qualifications.
From what you say, my initial suggestion would be that she worked in a chemist's shop. (Chemist = Pharmacist ). Since my GGF Bruce did similar, I can confirm that in the 1920s it was just about possible to do that without formal qualifications. GGF also referred to himself as a Druggist. Even by that time, regulations were coming in that mandated that certain substances could only be dispensed by formally qualified Druggists. Which he wasn't as I've checked the Registers. Nevertheless, there was still plenty of stuff that he could dispense and my father, as a little boy, would stand there wide eyed as his GF made up stuff on the brass scales.
I believe that the registers in question were: The Register of Pharmaceutical Chemists The Register of Chemists and Druggists The latter contains those with the minor qualifications - but I think that everyone in there had to have a formal qualification. The Society of Genealogists library has just 2 copies of the latter for the interwar years - nothing like as common as Medical Directories.
As already noted, a chemist could have been pretty much anyone preparing or dispensing pharmaceuticals or other preparations. The Royal Pharmaceutical Society has kept a register of chemists, druggists and pharmacists since 1868. They have the registers at their library in London, and can also run a paid-for search for you: http://www.rpharms.com/museum-services/research-service.asp
Unfortunately, they've recently moved premises, so the museum is not currently open, and the search is temporarily restricted to members only, but that will presumably change at some point. There's a little "Tracing people and premises in pharmacy" document at the above link that may be worth a look, anyway. It has information on the scope of work and approved qualifications in the field. In 1920 a degree certainly wasn't required.
(I had the search done last year, but they failed to find my GGGF, who probably retired just before the register was started. I hope you have better luck!)
MY great grandfather emigrated from Scotland in 1907 when he was 18 and in the 1910 census, his occupation was, like your great-aunt's, also listed as being a "chemist." My father told me that that meant he had been what we now call a "pharmacist" in a drugstore. Very unlikely that my great-grandfather had much schooling beyond age 17 but then again, "medicines" and the regulation and dispensing of them was likely very "unsophisticated."