The above link will bring you to an article provided by the National Institute of Health
Notice it says "treatment" not "curing." Nobody serious really makes that claim. But my DayQuil is only treating symptoms as well. Just like nobody says drinking plenty of water will cure you....but it's a good idea to do it . . . and you should.
Just in case any litigious bonehead is reading this: I am not a medical professional. Consult your doctor and blah blah blah . . . .
. . . . .since this is the age of tl/dr:
EOs are very interesting natural products and they possess various biological properties. An essential oil may contain hundreds of individual chemical components, mainly mono‐ and sesquiterpenoids, and phenylpropanoids. For therapeutic purposes, they are administered via inhalation (e.g. eucalyptus oil), orally (e.g. peppermint oil) and trans‐dermally (e.g. rosemary oil). Oils with a high phenol content, for instance thyme and clove, have antiseptic properties. Because of their wide‐ranging and complex effects, e.g. antibacterial, antiviral, anti‐inflammatory, mucolytic, bronchodilator, etc., they can be used as valuable materials in the treatment of different respiratory tract diseases. Some EOs are applied exclusively based upon long‐standing use, but some EOs can be used based upon well‐established use.
There are several in vitro techniques with which the antimicrobial activity of EOs can be tested. Today in vivo animal models of respiratory tract diseases offer good possibilities for testing their diverse biological effects. However, it should be highlighted that the number of well‐designed human trials is still very low. Furthermore, some studies have several limitations. Firstly, the small sample size may limit the interpretation of results. Secondly, short periods of treatments (e.g. 3 days) are not sufficient for the interpretation of results, as well. Another limitation is associated with the safety use of EOs. However, in some cases investigators did not observe any severe side‐effects, but larger‐scale studies should be designed in order to conclude the safety application of EO formulas. In addition, it is difficult to perform a double‐blind trial including EO or its individual constituent. Without a doubt, further studies, principally human trials, are needed to assess the efficacy and tolerability of EOs in respiratory tract diseases. More trials would also be important, because data coming from human studies may provide ideas for developing patents and might open novel perspectives for the development of products as well."
p.s. many many other scholarly articles of this nature can be found, with a simple search.