According to sister station KGO-TV in San Francisco, Jahi McMath, 13, was having her tonsils removed to help with sleep apnea Monday.
While in recovery, Winkfield says, Jahi had clots sliding out of her mouth.
Days later, she went into cardiac arrest and was declared brain dead.
Winkfield says hospital staff is now urging her to consider removing the 13-year-old from life support.
"They just have a social worker follow me around all day long asking me 'do you have any family that needs to see her?' like pushing a rush on it," said Winkfield.
Oakland Children's Hospital says any surgery procedure is risky, but will investigate McMath's case.
"We are very sad about this outcome, about what's happened to her, but at this point I have no information on the details of the surgery. We will certainly investigate what happened. In any surgery there are risks and there can be unexpected, unanticipated complications," said Oakland Children's Hospital spokesperson Melinda Kriegel.
KGO-TV contributed to this report.