Indeed, almost all cities have various psychological centers. In large cities, they are even of different orientations. For example, there are centers for low-income citizens. Consultations there are free of charge if certain certificates are provided. Without references, consultations there are several times cheaper (for example, in our city 100 - 150 rubles per hour). There are centers for the unemployed. There are centers for teenagers. For invalids. And others. Also, free psychological assistance can often be obtained at universities that have a psychological department. There, teachers and senior students provide assistance. In such centers, help is more like an appointment with a private psychologist or in a psychological clinic, while in social psychological centers, help is more often still aimed at solving the problems in which this center specializes.
As a last resort, there are psychological support hotlines. Help as such is unlikely to be provided there, but they will definitely advise on how to act in your case.
You can get free (or very cheap) psychotherapeutic help at municipal psychological centers. The help of a psychotherapist is not covered by insurance, so in the clinic you can only get a referral to a psychiatrist, whose appointment will be free, but he can only offer you to make an appointment with a psychotherapist or start taking medications (depending on the problems, this can be quite optimal and cost-effective option). The drugs are also not covered by insurance, you will need to buy them with your own money. Good luck solving the problem.