Your symptoms are all pretty typical of IBS. Unfortunately they are typical of other problems as well. For insance, given that you've missed a period, have you been checked by your gyno? There are a variety of "female problems" that can also cause bowel problems. Ovarian cysts, for instance, can make you sick and hurt. So can fybroid tumors and endometreosis. Unfortunately so can ovarian cancer. That's how they caught it in my aunt; she was having bowel problelms and pain and so they gave her an ultrasound, thought something looked not quite right in there and went in to check. Her ovary was covered in cancer, but luckily none of it had spread so they were able to take it out and she's fine. Thankfully, though, ovarian cancer is not very common in young women (my aunt's getting near 60).
Given that you hurt down low, has your appendix been looked at? That can cause pain, weight loss and sickness and it's very important that it's caught quickly as they can rupture and make you exceedingly and even life-threatening sick.
If your gyno tests and appendix come back clean, I would suggest you get a colonoscopy to look at your colon and see how it looks. If it looks fine, then you probably "just" have IBS. But you need to get scoped to make sure that you don't have an Infalmmatory Bowel Disease. It pretty much acts the same as IBS, but it inflames the interior of your colon and you have to take meds for it to keep it under control and try to keep it from damaging your colon.
Also, you should get a stool test done if you have been to any second or third world countries lately, if you live or work on a farm or with a lot of animals, or if you camp or hike and have drunk unfiltered water (like from a creek); these are all ways you can get an intestinal parasite.
If your doctor doesn't want to order these tests or refer you to a G.I. who will perform them, then you need to find a more able doctor. IBS is a disease of exclusion; when you've checked for everything else and have come up blank, then you can be sure you have IBS. Luckily, IBS is a lot, lot more common than worse things, like cancer or Inflammatory Bowel Disease. Chances are you have IBS, but better to rule out everything else first because everything else needs to be treated before it gets worse; you only have to learn to live with your IBS.