This is Dr. David
I am sorry about your dad and his throat cancer
HPV virus can't be spread by sharing a lollipop.
if you are worried about your daughter, you should get her gardasil HPV vaccine which is 3 shots which should be given to her before she is sexually active.
this vaccine can protect her against HPV virus for her life time and decrease chances for her to get HPV related cancers (throat, cervix and anal cancer)
let me know if you have other questions.
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HPV virus needs sexual contact and moist mucosal to mucosal contact to spread.
like during deep french kissing or sexual intercourse.