Can they use my personal sick time to take me to the doctor even though I'm still working?

Generally, personal sick time is intended for the employee's use when they are ill or unable to work due to health reasons. If you are still working and need to take time off for a doctor's appointment, you would typically need to use vacation time or unpaid leave, depending on your employer's policy. It's best to check your company's specific policies or speak with HR for clarification on how sick time can be utilized.