Hi! I believe I can be of help with this issue.
I can imagine how frustrating this situation must be for you. Her doctor is an authority, however the web seems to be telling a different story. You are clearly a loving parent and are right to try to make sure that you don't put your daughter into harm's way. Good for you.
More than likely what you saw on the web was reference to increased serotonin problems, maybe even serotonin syndrome, which is indeed scary. But it is also very rare. The reason for this possibility being brought up is that Zoloft is an SSRI and Cymbalta is an SNRI. Even though they act on the serotonin uptake system differently, they both are involved in that brain function. Therefore the worry and possibility.
But like with every medication you're weighing the risk/benefit ratio. And your psychiatrist is doing that and concluding what most doctors do: the incidence of anything as serious as serotonin syndrome is very rare. And furthermore, if she were to have adverse reactions, there would more than likely be time to withdraw the medications to avoid very serious consequences. And third, she is at a young age where her systems are strong and if there are adverse reactions and she has to go off the meds, she more than likely can handle that okay. So you see, your doctor is seeing a lot of upside in the benefit side, it looks like, and not so much downside on the risk side. This really is reasonable treatment thinking and most psychiatrists would agree with the approach as this combination of meds and classes of drugs happens not rarely at all.
You might also consider adding a behavioral component to your treatment for your depression and anxiety. While behavioral treatment requires more effort from the patient than medications and is not as quick acting, it doesn't have the side effects nor withdrawal symptoms of the medications. If you would like to introduce a behavioral treatment, feel free to ask me another question about it. Just write “For Dr. Mark” at the beginning and everyone will know it’s for me.
Okay, I wish you the very best!
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