I got rectal palpating, and doctor say i dont have hemorrhoid, but probably some tiny cut. the lube she used was in tube instead of one-time use packages, if she use the same pack of lube to check hiv infected patient before me, will i get hiv?

No-if proper technique is used. The lubricant is placed on a gloved finger from the tube then capped off. hands are washed after exam.

No, HIV transmission is not possible from inanimate surfaces. Check cdc.gov for details regarding HIV transmission.

No. Your doctor would have used a gloved finger to get the lubricant and discarded the glove after examination. She would not have touched the tube with her contaminated hand. Get HPV vaccine. Wish you good health! Safe sex: https://www.hopkinsmedicine.org/health/wellness-and-prevention/safer-sex-guidelines