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The corona virus disease 2019 (COVID-19) pandemic, which originated in the city of Wuhan, China, has rapidly spread to various countries, with many cases having been reported. Some existing antiviral agents showed positive results to inhibit the infection and transmission of the novel corona virus 2019 (2019-nCoV) in vitro. Covaxin is India's first indigenous COVID-19 vaccine. In this paper, we introduce the Gourava and hyper-Gourava polynomials of a graph. We compute the Gourava and hyper-Gourava polynomials of some specific class of graphs. Further, we obtain the Gourava and hyper-Gourava polynomials of some chemical structures viz., chloroquine, hydroxychloroquine, remdesivir and theaflavin which were used in the treatment of COVID-19. The Gourava and hyper-Gourava indices are investigated for the aforesaid antiviral drugs using polynomial approach. The Indian Council of Medical Research and Bharat Biotech announced that Phase 3 results of covaxin, developed by them, have shown an interim vaccine efficacy of 81 percent. So, the results obtained may be useful for finding the design of new medicine for the treatment of COVID-19. [ABSTRACT FROM AUTHOR]