“Why does my sister obsess over the idea of getting sick?”

Insist that she get a physical to reassure her. Perhaps someone in the family went through a traumatic event related to health issues and she holds on to that. She might need to be in a therapeutic group setting.

Dear Sister/Brother,

Thank you for your concern about your sister's fear of doctors and worries that something might be wrong with her health. You are asking why she is doing this? Without evaluating her, it would be difficult for me to say what is leading her to engage in those behaviors. Also, "whys" can lead one into spinning wheels! So, your focus needs to be on what can be done about the painful situation she is in. She definitely needs to go and see a licensed psychologist, preferably someone who specializes in hypnotherapy and cognitive behavioral therapy, like I do.  That will help her get to the root and origins of her fears and then release those fears so she can be happy again and enjoy her life fully.
Take care.

Dr. Lata Sonpal

Have her go see a therapist because she might have certain phobias and it could easily be psychological over anything. Sometimes a few sessions may be all she needs. Find a therapist who is not big on medication and treat her issues with psychotherapy.

Suggest you read this link - it may help you understand the situation better: https://www.everydayhealth.com/emotional-health/why-obsessing-over-physical-symptoms-could-equal-mental-illness-7477.aspx

Hopefully she will be open to seeing a psychologist once physical issues are ruled out.