Is it normal to have mild cramps and a pinching feeling in ovaries almost 1 week before periods start every month or is it something serious?

Very Normal: It's very normal to have this feeling in the ovaries monthly prior to the start of your menstrual cycle. If it happens every month it could be normal (physiologic) response to the hormones of your cycle, it could also indicate a problem with endometriosis. Regardless, a good 1st line treatment is ibuprofen, 600mg every 8 hours. If worried or debilitating then an ultrasound could allay your fear