DENVER (AP) — When the delta variant started spreading, Gina Welch decided not to take any chances: She got a third, booster dose of the COVID-19 vaccine by going to a clinic and telling them it was her first shot.

The U.S. government has not approved booster shots against the virus, saying it has yet to see evidence they are necessary. But Welch and an untold number of other Americans have managed to get them by taking advantage of the nation's vaccine surplus and loose tracking of those who have been fully vaccinated.

Welch, a graduate student from Maine who is studying chemical engineering,...