I struggle with bowel problems that give me the opposite problems to you - I've got unresolved complications from an autoimmune disease (coeliacs) that mean I have to eat specific things and take certain medications in order to not shit a 4/5 times a day, haha. And they say we have a divine creator, eh? But with being so ill, I've educated myself on probiotics, medications, and the frontier science that's currently taking place.
Honestly, with regards to IBS-C, your route for experimentation may well be in trialling probiotics like Symprove and VSL#3. They're pricey but can make a difference for some people. Do some research into the human microbiome. This is the place to start looking for medications and studies https://www.reddit.com/r/HumanMicrobiome/wiki/index - and get to know as much about it as you can. For now, maybe trial some pleasant over the counter probiotics like BioKult, Yakult, fermented yoghurts. If none of them make a difference then you can move on to the pricier, scientifically analysed stuff.
I'd also look into seeing if you can be prescribed products like Linzess or magnesium tablets for it. Movicol is another laxative brand to try. Moviprep is essentially an industrial strength laxative that you can't easily get hold of over the counter like you can with Laxido. A friend of mine takes Laxido, which is full of all sorts of things to make it taste nice, but with Moviprep they honestly don't give a fuck about the taste. It's designed to completely flush a person out ahead of an invasive medical procedure as opposed to making sure they can get through the day comfortably so things like taste and tolerance don't really factor into their thinking. I can't get the taste out of my memory even now, and the memory of how it tasted sits in the top of my throat whenever I think about it.
They're just about beginning to develop the science around this condition so the best we can do for now is go through a trial and error process until we each find something that works for us. Try removing certain known triggers of IBS-C (bread and high carbs, for example) for a while, try some probiotics, and eventually you'll find something that, one day, makes things a little easier. Until the day we're all rounded up by doctors and given a cocktail of pills that can cure gastrointestinal complications, all we can do is plough on and hope each visit to the porcelain throne is less painful than the last.
Also, get yourself tested for SIBO (small-intestinal bacterial overgrowth). They don't make a song and dance about it but you can get it done on the NHS now - I had myself tested at Salford Royal and it took about two hours. It came back negative but it's a process of elimination with bowel problems. Also, I'd recommend this YouTube series from a girl called Becky who struggles with IBS-C and took Symprove for 12 weeks to see what difference it made. She was eventually diagnosed with SIBO.