Teen refusing medication

Anyone dealt with a teen that is completely against being medicated for psychological/psychiatric conditions? I'm helping with my cousin who's being cared for by her ill grandma. It's a long story, but biomom is in prison, biodad is severly mentally ill. My cousin is almost 13. She's seeing a therapist and psychiatrist but has a very negative attitude against all mental health professionals from her dad and also heard and seen many negative things about psychiatric medications. She has been diagnosed with only anxiety and depression at this point. The doctor wants to see how a regular antidepressant/anxiety medication will help before diagnosing her with something else. He also wants to put her on sleeping medication because she has extreme insomnia. He hopes that if she's sleeping regularly, that will help the most. She absolutely refuses to take the medication. She's seen her biodad dealing with massive side effects of medications he's been on - which likely also includes seeing her dad's severe reactions to mixing his psychiatric medication with illegal drugs. The therapist and psychiatrist have been straightforward in telling her that the drug may work, or they may need to try another or a combination. She's very angry about being a human guinea pig. My cousin's behavior is completely out of control and she has been verbally abusive to her grandma. We need to do something, and hope medication will help. I don't have a very good relationship with her and she is very angry and hateful towards her grandma. She barely talks to the therapist. In the psychiatrist's lobby, she vomitted. We believe she's very anxious about mental illness being hereditary and being like her dad. But she will argue constantly that nothing is wrong with her. Her therapist isn't the best and she's been seeing him for 6 months now. I'm not sure if we should try to find someone she might trust more or if would be best to try to stick it out and hope he can help her accept treatment. Or if it's not working at this point, it would be best to find someone she might trust more.