A few suggestions:
Lately, we have been living in fear because of the violence in our city, state and country. It is growing frighteningly fast and people are always worried. Sometimes, we prefer to stay at home than to go out with our family and friends, scared about the news that we see every day.
Our politicians don't seem to be interested in this issue and don’t work hard to alleviate / mitigate this problem. I think the main cause of violence is impunity. Many times we see a person who has stolen, killed or committed any other crime and it takes a long time for this person to be sent to prison and sometimes he or she is not even sent to prison (this could be reworded to read "...and sometimes that does not even happen" to avoid repetition of "sent to prison"). This impunity makes other criminals think it’s easy to commit crimes and not be punished. It creates a domino effect and we are the ones who pay the price.
This is my opinion about this problem and I may not be right but if justice were a little swifter and impunity weren’t so widespread I really think the problem of violence would be much smaller than it is.
1) I have changed "arrested" to "sent to prison" because arrest does not encompass the act of being convicted in a court of law and sentenced to imprisonment.
2) The subjunctive mood requires "was" to become "were" in sentences like "if justice were..."
3) Some of the words in your text do not take the definite article ("the"). This also includes the title. ("Violence" instead of "the violence").