The reported number of US deaths from the Covid vaccine in Q1 2021 is 1,524. The average number of US gun-related murders reported per quarter is 3,679.
However, only 82.5 million people have been fully vaccinated for Covid, or 25.3 percent of the US population. Even if we ignore the fact that the vaccine deaths are almost certainly underreported, this means your chances of dying from being vaccinated for Covid are 63.7 percent greater than your chance of being shot dead, and 44 times greater than your chance of being shot dead by a police officer.
Perhaps that will help put things in perspective. If the government actually cared about lives, they would devote more effort to vaccine control than they do to gun control.