I would wait at least 2 weeks to make sure that the pill is in your system and give it time to start working. Your body will have to adjust to the new pills.
You should consult your doctor and pharmacist with this issue. Also, you want to read all of the materials that came with the medicine. It is probably fine for you to have sex right away. Howevern, I personally would wait at least a month before doing so.
My doctor told me that it takes a new birth control 90 days to fully work. However, she said I should be okay after a full two months of taking the new pill. I only waited two months after switching and everything worked out okay for me, but every body will react differently.
If there was no time in between, you are protected from pregnancy. The pill works by fooling your body into thinking that it is already pregnant. If there is no decrease in hormones (as there would be if you stopped taking them), your body still "thinks" it is pregnant.
I would strictly contact the provider of the birth control pills regarding that question as it might also entail where you are in your cycle. Or call your doctor.