So I am in my first month of being on the pill, and last week on Friday the 7th and also the 8th I had unprotected sex. And yesterday, Friday the 14th, exactly a week after the unprotected sex, I was due for my period but it did not come and still has not. Yesterday morning I started feeling sick before I had taken the sugar pill, and today I actually threw up, but I also have been getting period like cramps. Is it too soon to be feeling symptoms? Could I possibly be pregnant? Will a pregnancy test come up negative even if I may be positive because it's only been a week?

Sure you could be pregnant...you had unprotected sex...that's how it works.

Are you pregnant? We can't know that. You will have to wait it out and take a pregnancy test in a few weeks if you don't get your period.

It could be due to starting the pill... different ones can effect people differently, especially when first starting them, including altering your cycle.
Obviously, as odinn7 said, it could be pregnancy. See what happens in the next few weeks.

If you started taking daily birth control pills,
1. you know they are normally not effective the first month, and you needed to use protection till the second month
2. you know they are not 100 percent effective anytime
3. the pill will control period date, when you stop them or use sugar pill for that week... so where on the pack of pills are you?
4. the pill when first starts can alter period due dates
5. anytime you have sex, you can become pregnant.
6. it is too early to test, it would still show negative, even if pregnant at this point.
You need to wait, till you are two weeks late, and then test.