Here's a few for depression and air pollution[1][2]
Here's some studies on anti-inflammatory treatments for treatment resistant depression[3]
And more relevant to the original topic, 5HT-2A receptor agonists may have anti-inflammatory effects. There's huge potential in a broad class of molecules that have been banned for moral, not medicinal, reasons.[4] Edit: picked another one [5]
Sorry, but none of these are studies about the relationship between depression and inflammation treatment.
Such a study would have to provide a measurement of the severity of the depression. Then split the patients in two groups. Give one group a placebo and the other one the inflammation treatment. And then compare the depression severity in those groups after the treatment.
It's a medical journal, Trends in Immunology, the same type of journal that all medical studies are published in. Unfortunately we still have a broken publishing system in the US so it is insanely expensive to read articles/studies published in these journals unless you work somewhere with an institution-level account.
1. https://www.ncbi.nlm.nih.gov/pubmed/30719959
2. https://www.sciencemag.org/news/2017/01/brain-pollution-evid...
3.https://www.healio.com/psychiatry/depression/news/online/%7B...
4.https://www.fasebj.org/doi/abs/10.1096/fasebj.2019.33.1_supp...
5.https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3788795/
That's just some quick googling. There's tons more out there to read!