I had a mole shaved off three days ago. Is Betadine okay to use?

Betadine isn't going to help. You want to keep the area moist - and Betadine doesn't do this. Clean the area like you are doing and apply either Polysporin or Vaseline to the site, and then cover it with a bandaid. Keeping the site moist will help alleviate scarring and divets. "This answer has been solicited without seeing this patient and cannot
be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."

After a shave excision of a mole, I advise my patients to keep the area
clean by gently washing twice daily with soap and water and then applying
either plain petroleum jelly or Aquaphor Healing Ointment. Band aids are
optional after the first day. Application of an antibiotic ointment or Betadine is NOT
recommended.