I really feel for you. My son was very similar.
Main thing with kids that struggle like this - do not sleep train. Kids brains are developing so much in the first 3-4 years and they need us. Sleep hygiene is different and a good routine / good sleep environment / appropriate wake windows is helpful and not cio.
i would agree with the other poster - children’s chiropractor or osteopath would be my first point of call. If your LO hates the carrier and the car seat and the pram and being rocked, sounds like they might be uncomfortable/ in pain. My son was night and day after seeing one (he had torticollis and I noticed something wasn’t quite right after he started using one arm for everything- which they shouldn’t do until 2). Now he was still difficult to get to sleep but massive improvement.
you could even try giving calpol (as a one off) 30mins before a nap is due (when not overtired) and seeing if that helps sleep - if it does then you can get a feel that pain is the issue and book an appointment with an osteopath. (Don’t bother with the NHS they’d have happily let my LO end up massively delayed before they offered physio).
2nd - try the huckleberry app and pay to get the sweet spot (or whatever it’s called) to advise you on perfect wake windows. This helped us sooo much. I was basically trying to get him to sleep after he was tired - but starting before he was tired was a game changer (again still difficult but doable)!
3rd - you’ll probably find that when LO goes to nursery / childminder they’ll sleep like a bloody dream and you’ll be so annoyed but also so relieved. So hopefully you won’t be long before you get that break.
another one to look into if there are any other issues - dairy intolerance. My LO has CMPI and took me 14 months of him having silent reflux, very loose stools, wind, sleep problems and being on an adult dose of very expensive medication - for the gp to stop telling me he didn’t have any dairy problems and refer me to the peads dr who immediately said yes he’s got cmpi you need to cut out diary (only been telling them that since he was 2 weeks ok).
try following Nurturedfirst on Instagram (plus the heysleepybaby recommendation you got). Her account is great and really helped me to reframe my frustration and be calmer. Her mantra is ‘this is important’ and it’s amazing how just saying that to yourself can really help chill you out.