As you had intercourse soon after your period, you were still in the safe period and there is no cause to worry; moreover, you have no risk at all as you took the emergency pill. Please remember that the emergency pill contains excess hormone and could cause some amount of breakthrough bleeding
and it is likely to disturb your next cycle. In the current situation, it would be advisable not to switch the birth control pill you have already started taking as changing the pill in the middle of a cycle is not going to give you any protection for that cycle and is likely to cause menstrual disturbances. You may take the advice of your consultant for further assistance. Hope this helps. Take care.