Would taking the wrong birth control pills affect my health drastically?

Probably not: Any commonly prescribed oral contraceptive pill will be safe for most healthy young women when used correctly. "Drastic" adverse effects are rare. Different forms will be tolerated differently though and may be more or less effective at controlling spotting, menstrual pain, heavy bleeding, etc or may have varying impact on mood. A trial and error approach is often used to find the best fit.