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Caveat: I'm not a doctor, just a mentally ill nerd. Don't take anything I say as gospel truth.
Sertraline is the default SSRI because there is a good evidence base across a wide range of conditions, the risk of serious side effects is relatively low, it is well tolerated by most patients and it costs pennies.
There is a very long list of alternatives that you might get on better with. If you go back to your doctor and say that you're not doing well on sertraline, they should offer an alternative drug. You might also want to consider the timing of your dose - sertraline should be just as effective if taken at night, but the side effects may be much less of a problem.
In your case, interaction between your medications is likely to increase the risk of some side effects and make prescribing more difficult. I'd be slightly concerned about the interaction between amitryptiline and sertraline, as there is a risk of serotonin syndrome. If at you feel extremely hot and agitated, you should stop taking both drugs and seek immediate medical attention.
It might make sense to try switching the amitryptiline for an SNRI or an anticonvulsant. Several drugs are effective for the treatment of both neuropathic pain and anxiety, so you may be able to kill two birds with one stone. This would reduce the risk of side effects from drug interactions, but your neuralgia symptoms might briefly increase while you're switching drugs. Duloxetine or pregabalin would be plausible options. If you think this might be worth trying, discuss it with your doctor.
We don't really understand how or why antidepressant drugs work, so there's a lot of trial-and-error involved in prescribing. Most antidepressants can cause either drowsiness or insomnia depending on the patient, which is just weird. There's also an element of matching the right side effect profile to the right patient. Some side effects can be beneficial to some patients.
If want to swot up, you can read the NICE guidelines for Generalised Anxiety Disorder at the link below. These guidelines are the standard treatment approach that doctors are expected to follow. The guidance for drug treatment starts at paragraph 1.2.22.