Although you don't sound like you are bleeding, the vacuum created by the bottle might have been strong enough to exert a lot of pull on your interior structures. You might have strained or stretched muscles or tubes in the area, or the colon. Because it's been three weeks with no improvement, you probably should see a doctor. What you can say to your parents is that you have lower abdominal pain, or intestinal pain. You don't have to explain to them what (you assume) caused it.
There are a lot of unremarkable issues in the lower intestinal tract to see a doctor about, including urinary-tract or kidney infections, constipation, or hemorrhoids. There are also more serious things that aren't sexual, like chronic appendix inflammation or intussusception in the intestine. If you feel your parents will grill you about what's wrong, you could look up some of those ailments and describe those symptoms to your parents. But, most parents will accept their son's word that he needs to see a doctor. Just say that you have pain, and it's been hurting for three weeks and hasn't gotten better. That should be enough.
Also, (if you didn't know this), when you get to the doctor's, you have the legal right not to have your parents be in the room when you are talking to the doctor. (And, don't be embarrassed, doctors have heard everything it is possible to do to yourself.) Your parents might be surprised to hear you don't want them to be in the exam room with you but you have that right, and the doc will enforce it if you ask. They will probably write it off as you being embarrassed to talk about issues "down there" in front of them, and you'll never have to tell them what you did. When you do explain what happened, you might ask the doctor if there is a possibility of getting an MRI to make sure you didn't accidentally pull something around that shouldn't be pulled around.
In the future, remember, put nothing up your back door that is open on one end and closed on the other, as it can indeed cause vacuums. Some women have actually given themself uterine prolapse by doing the same thing. Either your object should be closed at both ends, or open at both ends, and should be relatively conical (not bumpy) and not small enough to get lost. My sister was an EMT and once had to take a guy in who had a carrot stuck up his behind. Don't be the carrot guy.
Good luck, I hope it's nothing serious.