Having previously suffering same as you, i actually ended up in a&e 3times in 3 months.
I jave had so much different medical advice from gastroenterologists and other HCP's. One told me to eat low fibre, low fat. Another to concentrate on fruit and veg that crunch when you eat them, another to carry on eating exactly how I do approx 8 fruit and veg portions a day.
There could be a number of reasons for constipation.. Another reason can also be not drinking enough water..
Not much advice about whether low carbing is cause or not, because I got mine even though I eat really healthy with fruit n veg, I have never low carbed. My only concern would be that you should eat veg or fruit to get a fuller range of essential vitamins. I am a believer in a balnced diet of white meat/fish and veg for main meals, I dont have pasta, rice or potatoes but thats not because of liw carbing. I do eat bread, pancakes etc.
I found dulcoease one of the best things. However my probs stopped or eased up so far, when I stopped eating jelly babies as hypo stoppers...