Within minutes of getting the Johnson & Johnson Covid-19 vaccine, Michelle Zimmerman felt pain racing from her left arm up to her ear and down to her fingertips. Within days, she was unbearably sensitive to light and struggled to remember simple facts.

She was 37, with a Ph.D. in neuroscience, and until then could ride her bicycle 20 miles, teach a dance class and give a lecture on artificial intelligence, all in the same day. Now, more than three years later, she lives with her parents. Eventually diagnosed with brain damage, she cannot work, drive or even stand for long periods of time.

“When I let myself think about the devastation of what this has done to my life, and how much I’ve lost, sometimes it feels even too hard to comprehend,” said Dr. Zimmerman, who believes her injury is due to a contaminated vaccine batch.

The Covid vaccines, a triumph of science and public health, are estimated to have prevented millions of hospitalizations and deaths. Yet even the best vaccines produce rare but serious side effects. And the Covid vaccines have been given to more than 270 million people in the United States, in nearly 677 million doses.

Dr. Zimmerman’s account is among the more harrowing, but thousands of Americans believe they suffered serious side effects following Covid vaccination. As of April, just over 13,000 vaccine-injury compensation claims have been filed with the federal government — but to little avail. Only 19 percent have been reviewed. Only 47 of those were deemed eligible for compensation, and only 12 have been paid out, at an average of about $3,600.

Some scientists fear that patients with real injuries are being denied help and believe that more needs to be done to clarify the possible risks.