Have you tried taking an iron supplement? (Have you ever tried to donate blood and been told you were anemic?) It sure sounds like anemia to me.
So, you should see your doctor to discuss this. Is the first day of your period heavy bleeding or spotting? How does your cycle go typically? That it is far less when you are on birth control pills seems to me that this is hormonally related and hence, can see why the suggestion is that it is PMS.
Ladies, look up period flue. believe it or not, your cycle can cause this due to the release of prostaglandins prior to period. Nausea during period is not uncommon. www.ladycarehealth.com/causes-and-treatment-of-menstruation-nausea/ It is also not uncommon to get dizzy right before your period and it wouldn't be a stretch to be dizzy the first day of your period. https://www.healthline.com/health/womens-health/dizziness-before-period. Pale I don't know about but if you are dizzy and nauseated, pale wouldn't be out of the question.
I believe this all related to your hormone balance and I'd get a simple blood test to see if anything sticks out one way or the other. good luck