Menstruation happens from the uterus on down, and the Fallopian tubes are above the uterus. So menstrual cycle irregularity would not relate to having blocked tubes. Ovulation tests would not tell you whether tube (which are below the ovaries) are blocked. There is not a blood test that will tell you if a tube is blocked, it's like a traffic jam in your duct. Why don't you want to do an hsg?