I get severely anxious and depressed when I get my period. Sometimes I want to quit my job because of it. How can I manage this stress?

Premenstrual anxiety. Severe menstrually related mood and anxiety symptoms sometimes respond to antidepressants given for just a few days a month. It is also helpful to chart your mood for a few months, to figure out the timing of when you might need the help. The web site for the depression and bipolar support alliance (dbsa.Org) has an easy to use mood chart in their "wellness toolbox" you might check out.
Exercise. Exercise is a great way to relieve stress. Your body releases endorphins during exercise, which can help you feel calm. If you exercise 30 - 60 minutes a day, your stress levels can improve. When stressed, take 5 slow, deep breaths with your eyes closed, then roll your shoulders forward 5 times, then back 5 times. This will slow your heart rate and release tension in your neck and shoulders.