I am not a doctor but Plan B is an emergency contraception that prevents a fertilized egg from attaching to the lining of the uterus. I do not know where you are from, nor do I know the availability of Plan B where you are at.
There is VERY little chance you could be pregnant due to "dry humping" but since precum was involved, you should take a test anyway. You do not have to see a doctor to find out if you are pregnant or not, you can buy a pregnancy test from your local drugstore/supermarket.
Chances are your late period is due to stress. But if you take a pregnancy test and it is negative and still no period, it would not hurt to go to the doctor to make sure you are okay down there and that something else is not going on.