First of all since no one bothered to comment on what I caught as the most important part of your post...
Killing yourself, even if you are only 1/2 serious, would never be a good resort to anything. If she was pregnant and it is yours, parents, believe it or not are pretty accepting of mistakes, even if it takes time. If it really is an issue and you are really troubled, talk to your mom (or dad), you may be suprised. She will also be proud of you for trying to be so careful. You are 16, not 12.
Now, I agree with alot of what has been posted here. Never use 2 condoms, if you are looking for added protection, add contraception foam, such as delfen to the use of a condom. Don't stop using condoms until you are ready to have children and are paying your own health insurance incase you contract a disease. Ok, that having been said, of course its possible to get pregnant your first time. However, highly unlikely you pegged that timing perfectly. Most likely at 16 her periods are not regular as it is, so if she is late, thats hard to tell, I bet even for her. Now, vomiting would not be happening already, that doesn't usually hit until 7 weeks or so. Eating constantly or always hungry, well I have to say I don't know a 16 year old, boy or girl who isn't always hungry. She would be more apt this early to not eating as much.
Now the hard part. I also agree with the postings that she may in fact be pregnant, and further along having real symptoms. If this is the case you are being "had" and she was not a virgin (guarantee you wouldn't know the difference and I don't mean that as an insult) and she is using you for two reasons, she doesn't want you to know she cheated on you and wasn't a virgin, and you are the nice guy who will help her through this emotionally and financially.
Try not to worry, talk to your mom if it continues and don't give her (girlfriend)so much attention about it. If she really is you will have family support through whatever you choose to do. However, just a suggestion, from a legal standpoint depending on whatever state you are in, claiming fatherhood (even if it ends up being someone else's baby) makes it easy for her to make you financially (or your family) responsible. If you say it is your baby at anytime, its difficult to court order her to have a paternity test done on the child. This is all hypothetical, but if she is, and its born, wait until after a paternity test is done to offer up anything financially. Giving her money (in some states) is basically accepting parenthood. I am not saying don't be responsible, I am saying be smart.
But that is all heresay. I highly doubt she is pregnant.
Good luck