Plan b and the pill

My boyfriend and I had sex yesterday and the condom broke without either of us knowing we immediately bought the emergency contraceptive pill and took within an hour of having sex. I have an appointment to go to family planning and get put on the pill but will the doctor allow me to go on the pill or will they make me wait 4 works to ensure I’m not pregnant. I’m worried as my mum doesn’t know what happened and I don’t know what to say to her if the doctor tells me I can’t go on the pill yet as a precaution in case the emergency contraceptive pill wasn’t effective ? Help me please