Hello, Here's The Situation. I Have Been On Birth Control

Hello,

Here's the situation.

I have been on birth control for two months.
Recently I just switched to a new kind, so I finished my week of placebo pills, and finished my period a few days before the placebo pills ended. I then had to wait 1 day to start my new pack of birth control, of which I am now 2 days into. Around the same time I had unprotected sex with my boyfriend- he is on meds that make him kind of numb right now so he said he couldn't tell if he was "leaking" or not during sex. He didn't cum but it is possible that precum came out. Am I protected, since my period just happened? Or do I need to seek out emergency contraceptive? I would prefer to use my old pack of birth control, Sprintec, which contains .250 mg norgestimate and .035 mg ethinyl estradiol in each pill for 3 weeks. Can I take some of those combined?

Long story short- am I unprotected, or okay since birth control takes a while to get out of your system and I had just gotten off of my period? Just being extra cautious. Do I need to combine some Sprintec pills then continue with my new birth control?

Thanks!