Are the continuous brown discharges that started around May 20th, increasing in quantity and becoming darker, accompanied by lower back pain, considered menstruation or not, and what is their ruling?

These dark brown discharges are considered "kudrah" (brownish discharge), and according to the Maliki school, whose madhhab is prevalent in the questioner's country, "sufrah" (yellowish discharge) and "kudrah" take the ruling of menstrual blood. Menstruation, according to them, is defined as: "Blood, whether yellowish or brownish, that issues by itself from the private parts of a woman who is habitually capable of conception." Imam Malik states that if a woman sees yellowish or brownish discharge during her menstrual period or otherwise, it is considered menstruation, even if she does not see blood with it. Therefore, what the questioner has seen is considered menstruation, and she must refrain from prayer and other acts that require purity while these discharges are present, until she sees a sign of purity, whether it be complete dryness of the area or the emission of a white discharge ("qassah bayda'").