Help! Pill and protection!

So I have been on a BC pill for past 2 months but I got it switched today cause I was having issues with it and my doctor asked if I was sexually active which I said no cause my mum was there (I’ve anxiety and stuff) She told me to start this new one today (I’ve been taking the other one up until today) but now I’m meeting my FWB next week and I don’t know if I start the new pill today if it’ll work as a protection or what cause you usually start it on a new period but doctor said to just start today. Help!