No, really not. Why not go for a more robust falsehood "Vax turns you into a wombat" or something of the sort?
https://www.muhealth.org/our-stories/does-covid-19-vaccine-affect-fertility-heres-what-experts-say
However, the risks of a Covid infection for pregnant women and for women with small babies are well documented.
https://www.cdc.gov/coronavirus/2019-ncov/need-extra-precautions/pregnant-people.html