Zoloft adding Cymbalta. Is tapering necessary?

Interactions between your drugs
Major
sertraline DULoxetine
Applies to: Zoloft (sertraline), Cymbalta (duloxetine)
Using sertraline together with DULoxetine can increase the risk of a rare but serious condition called the serotonin syndrome, which may include symptoms such as confusion, hallucination, seizure, extreme changes in blood pressure, increased heart rate, fever, excessive sweating, shivering or shaking, blurred vision, muscle spasm or stiffness, tremor, incoordination, stomach cramp, nausea, vomiting, and diarrhea. Severe cases may result in coma and even death. You should seek immediate medical attention if you experience these symptoms while taking the medications. Talk to your doctor if you have any questions or concerns. Your doctor may already be aware of the risks, but has determined that this is the best course of treatment for you and has taken appropriate precautions and is monitoring you closely for any potential complications. It is important to tell your doctor about all other medications you use, including vitamins and herbs. Do not stop using any medications without first talking to your doctor.
Report: https://www.drugs.com/interactions-check.php?drug_list=949-2273,2057-1348

Source: Drugs.com

How to switch antidepressant
Doctors use four different strategies Trusted Source to switch people from one antidepressant to another:

Direct switch: In a direct switch, you stop taking your current drug and start on a new antidepressant the next day. It’s possible to make a direct switch if you’re going from an SSRI or SNRI to another drug in the same class.

Taper and immediate switch: In this switching method, you gradually taper off your current drug. As soon as you’ve fully stopped the first drug, you start taking the second drug.

Taper, washout, and switch: This is a conservative method of switching in which you gradually taper off the first drug and wait for it to leave your system before switching to the new medication.

Cross taper: You gradually taper off the first drug while increasing the second dose. This can be beneficial when switching to a drug in a different antidepressant class.
The strategy your doctor will choose will depend on factors such as:

The severity of your symptoms: It isn’t safe for some people to go off their antidepressants for
several days or weeks.
Concerns over symptoms: Cross-tapering can help prevent you from having withdrawal symptoms.
Which drugs you take: Certain antidepressants can interact in dangerous ways and
can’t be cross-tapered. For example, doctors won’t combine clomipramine (Anafranil) with SSRIs, duloxetine (Cymbalta), or venlafaxine (Effexor XR).

Source: Healthline
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I know there is a lot of information you have to analyze and discuss with your Dr./Psychiatrist.
Remember, you are paying your Dr. for a safe and effective treatment for your conditions, you will be the one experiencing this switch, and you want to minimize any potential risks involved, so once again, you have a saying in whatever your Dr. is planning on doing, you do what gives you peace of mind, you don't need the extra anxiety this "switch" is causing you.
This is a joint decision between you and your DR. , nothing is free in life and everything comes with a cost.
Having said that, instead of given you a pep talk, I have provided all the information I thought necessary for you to make your own choice along with your Dr..

All the best, masso