what are the odds?

I started my birth control on Sunday march 12th. The papers it came with said it would be in effect 7 days after I began it. Yesterday was Saturday march 19th and I had finished my first weeks dosage. Yesterday things also got pretty heated with my boyfriend but we had no condoms so I let him put it in only for a couple strokes before I made him get out. His dick was dry there was no precum, but there was some a little before it happened. Long story short I just wanna know if I should go out of my way to get an emergency contraceptive since I'm the most paranoid person alive. I just finished my period a few days ago and this app said my fertile window would start in 2 days if I wasn't on the pill. I just wanna know how many precautions I should take, because I always hear that I should use backup protection for about a month after starting, but the papers said 7 days so I don't know I'm just freaking out😬