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I guess you are taking combination pill that is hormonal contraceptives containing both estrogen and progestin (synthetic progesterone). These act by preventing your ovulation and making your cervical mucus thicker.
You need to take combination pills within five days after the start of the period. Then, you need not follow other means of contraception.
You may start combination pills at any time and only concern is that you will be protected from pregnancy 7 days from then.
Yes, you need not take pills in the fourth week and this will initiate your withdrawal bleeding that is you will have a menstrual bleed in that week and you will be protected.
Some measures you need to follow. You need to ensure that you take these pills regularly at the same time each day.
If you vomit immediately following pill consumption, then take one more pill. You should not miss the pill. If you miss a period, then do not panic as irregular periods are common. You need to confirm by urine pregnancy test
For further doubts consult an internal medicine physician online --> https://www.icliniq.com/ask-a-doctor-online/internal-medicine-physician