The kidneys release a lot of fluid on low carb diet, that may be why you’re going so much? Either that or a uti can cause the frequent urination. Are you drinking more fluid than usual? As far as constipation goes that’s common on low carb. More fiber like low carb veggies, and maybe some magnesium caps to help. You need more sodium and fat on low carb too, that might help with the sick feeling. I did low carb years ago, it can be challenging in the beginning. Calorie counting is just as good though too. If you can’t feel better after a month on low carb, then maybe it’s not for you?
I guess that can happen, not always to everyone though. I usually go high protein and low carb to look my best/ get the ladies. Doesn’t really have a bad effect on me.