I think that you are totally in the right to be frustrated by your girlfriend's actions.
First oh all, as mentioned, having a pregnancy test show positive a week after conception is impossible. It fankly cannot happen. Even tests at doctor's offices take longer than that. How Long From Conception Is Implantation?
Pregnancy Test Sensitivity and Early-Detection Testing | Ovulation Calculator
Generally, if an egg is going to be fertilized and conception is going to occur, it will have to happen in a 24-hour period after ovulation...Once the egg is fertilized, it will travel to the uterus for implantation...The process of traveling and implanting will take somewhere around 7 to 10 days altogether...Thus, it is possible that it can be as many as 7 to 14 days between the time of sexual intercourse and the time that the fertilized egg implants in the uterus.
The most sensitive pregnancy tests can detect hCG levels at as low as 20 mIU - or at around 8 days following implantation of the egg...If a woman is pregnant, the amount of hCG in her system should be around 25 mIU at 10 dpo (days past ovulation), 50 mIU at 12 dpo, 100 mIU at around two weeks dpo...Drugstore pregnancy tests generally detect pregnancy at 50 mIU - 100 mIU hCG, though you can find early-detection pregnancy tests on the Internet with sensitivity levels as low as 20 mIU.
If your girlfriend has used pregnancy as a means to gain attention or somehow to keep you around, that is a serious issue, and not one that you need to accept. Whether or not you two are having sex, she really needs to figure out a way to not keep stringing you along in this manner.
If she genuinely thinks that she does keep getting pregnant, then she really needs to look into a better method of birth control (I'm on The Pill, and love that, but there are a ton of other methods of birth control
available). It's not fair to herself or to you to continually put you both in this position. It's emotionally and physically draining to have pregnancy scare after pregnancy scare.
If she isn't being honest about this, then that's not something I'd recommend dealing with. She would obviously have some sort of issue with attention that is well beyond what you should be expected to deal with.
Honestly, I wouldn't even bother to stick around "just in case" she is pregnant (because I doubt she is). I wouldn't worry about any legal recourse (although you both are likely under the age of consent, I have not heard of a case of prosecution due to underage sex when neither partner is of the age of consent).
You need to do what's right for you. And, to me, it sounds like this girl is not right for you.