My wife’s theory is there would be less hesitancy if the vaccines were being distributed through people’s primary care physicians instead of at mass vaccination sites or Walgreens. People may distrust the media, the government and all sorts of other nebulous groups, but they largely trust their doctor.
You can almost certainly get the vaccine from your physician, and you can also call your physician’s office and leave a message asking them whether you should get vaccinated. They’ll call you back.