Firstly, if you're eating only 15-20g carbs, then you will be losing weight!
Secondly, if you're drinking the amount of water that you should be, then the ketostix are a waste of your money, as they won't show up dark purple.
When you say you're having trouble pooing, do you mean that you're just not going as often, or is it painful/difficult to pass? If the former, then don't worry. If the latter, then this also indicates that you're not eating enough vegetables and salad, aka carbohydrates! Make sure you're getting plenty of veg like broccoli, cauliflower, celeriac - all good and low in carbs.
Things that can help - strong coffee, a high strength vitamin C tablet, exercise, drinking more water/eating more fat.
Can you list out for me what your meals have been like over the last few days, and also how much water you've been drinking each day?