Medical research has not identified uncontrollable shaking as side effect of the vaccine so far.
However, Wired reported that "Skelton herself published a picture of what appeared to be a US Centers for Disease Control and Prevention (CDC) vaccination card on her Facebook profile on January 16. But the vaccine lot that she was administered according to the card does not appear to have been linked to any report of vaccine adverse reaction in Indiana, according to VAERS, the reporting system run by the CDC and the Food and Drugs Administration. In fact, all eight cases of adverse reactions to any Covid-19 vaccines reported in Indiana since the start of 2021 involved people over 60 – Skelton, according to her vaccination card, is in her forties."
The article further states that "according to Skelton’s posts, the doctors that visited her when she was hospitalized for her tremors on January 11 ruled out that the Moderna vaccine could have played a role. One doctor from Deaconess Orthopaedic Neuroscience Hospital, the facility where Skelton was treated, though not someone who had treated her personally, told the local press that shaking is not one of the known side effects of the Moderna vaccine. According to the CDC, side effects can include pain or swelling at the injection site or fever, chills, or a headache, all of which resolve in a few days." On January 12, Skelton wrote on Facebook that doctors said her shaking resulted from a conversion disorder, a mental condition triggered by extreme stress, but she remains unconvinced.
Medical experts have cautioned that as more people get vaccinated, it is likely that more stories will surface of people claiming several side effects. It is important to determine a causal relationship between the symptoms and the vaccine before making claims. As of now, whether the vaccines brought on these symptoms remains to be proven; however, so far, there has not been any report that establishes a link between the COVID-19 vaccine and uncontrollable shaking. With 51 million doses of the vaccine administered globally so far, medical research has not identified these symptoms as side effects of the vaccine.
The COVID-19 pandemic has given rise to a lot of potentially dangerous misinformation. For reliable advice on COVID-19 including symptoms, prevention and available treatment, please refer to the World Health Organisation or your national healthcare authority.