It's indeed a possible side effect of iron pill use. So long as you don't have any other adverse reactions to the pills, I hope that this doesn't dissuade you from their use. Interestingly, some experience (and perhaps you are) a condensing of the fecal matter as a result of the pills as well. This, too, is of little concern and can be kept in check by increasing raw vegetable matter. It should be noted, however, that iron pills are especially slow to metabolize into useful iron ions in the body, some estimates as high as six weeks depending on individual body chemistry. Don't despair--the immediate effects are those you are experiencing now.
A more effective way to get the iron you are looking for in an already usable form would be to increase your consumption of very dark green vegetables. (Red meats provide only limited-use iron ions.) Spinach is a good one, kale is even better. Cooked or mixed into salads, these also have many other vitamins that iron pills lack (as well as the other side effects you noted). Also, because they appear in a variety of forms in the vegetables, they are accessed almost immediately. If you don't like vegetables--and you should!--many breakfast cereals are fortified with iron filings to meet the daily allowance (like Total and lots of kid's cereals) that your stomach converts to usable iron in the stomach with your hydrochloric acid. The cereal method, however, might be used in conjunction with vegetables because of the increased sugar and simple carbohydrates you will find in them. Nonetheless, it's still a viable way to get iron.
Whatever the method, check some fresh green veggies out, try some cereal and see what works. You might still take the pills on a limited basis (every other day) to supplement your foods. Remember that red meats, while higher in iron, are still lower in iron than these other options as well as exposing you to a number of unsafe fats and cholesterol that, amusingly, can interact negatively with iron absorption. White meats have even less iron.
Good luck! Make sure to drink plenty of water with the pills!