The fluttering feelings, and feeling like something is moving around in you could also simply be gas. There are a lot of things that can cause excess gas, including beans and raw veggies (and some cooked, especially al dente). You may be developing a lactose inolerance; try cutting out all dairy products to see if that helps with both the gas and the constipation. Also, if these feelings, especially the constipation, are timed to coincide with your cycle, that may be the sole cause of the problem; a lot of women have bowel problems and other weird digestive problems when they get their periods. You are still young, so you may grow out of this. If these problems definitely seem connected with your period, and they get worse, or don't go away in a year or two, then you may want to see about trying birth control. Sometimes, when women have really heavy periods or a lot of period-related problems, birth control pills can help them balance out to where they are more normal.
Also, do you ever eat anything that's sugar-free or reduced-sugar, such as diet/diabetic candies, ice-cream or even no-sugar gum or mints? All of those products contain sugar alcohols and sugar alcohols give a lot of people gas, and frequently diarrhea too. But if you are only chewing sugar-free gum or mints, you'd probably only be getting enough sugar alcohols to give you gas. If I ever have any, I get a very horrible fluttering sensation in my guts, like I have a live bird trapped in there. Even if they aren't the root cause of your problem, they will make whatever bowel problems you have worse, so never consume them.