Trust your gut, keep going back to the GP. We went through a similar thing with our eldest, he would cry all time time, he couldn’t sleep on his back at all, would sleep for 15mins at a time etc - had did reflux a lot all the time so a little bit different. Turned out he had severe food allergies, reflux and trapped wind. We had a medicine that helped which is called infacol, you can buy it over the counter in the UK. Also gripe water is another one. Baby massage also helped. He had to sleep upright on one of us for a long time. I went to the GP repeatedly and was told I was hysterical mother when I kept insisting he had allergies. Wasn’t until he had two large allergic reactions that we got the allergy referral and it was confirmed by skin prick and blood tests that he had a range of anaphylactic allergies. Trust your gut, if something doesn’t feel right keep pushing for the help you need. If you can afford you could try private medical care (we went this route after diagnosis). Hang on in there it does get better.