Ohh God this is bringing back memories for me! In answer to your question, YES! Both of mine cried whenever they were awake.
DS2 would only sleep on my chest and screamed and cried if I dare move. Nothing soothed him in the day, no amount of rocking, shushing, cuddling, feeding, he just was inconsolable all the time for HOURS and hours.
DS1 was easier to get to sleep at night and he did sleep in his moses basket but he cried all day, every day. I walked around with him in a sling but he hated it after a few minutes, I pushed him in the pushchair, he cried, he hated the car seat, hated being sat on my knee, he just cried and cried and cried. I took him to the doctors, health visitors, cranial osteopath, paediatrician, tried him on reflux medication, dairy free diet. Nothing worked and everyone just said he was a 'fussy' baby. The only thing that soothed him was the be placed up right over my shoulder while I walked back and forth with him, which I did for hours just to get peace but the second I put him down or stopped moving, he started again.
I thought I was doing everything wrong, convinced myself my baby hated me, I got extremely depressed and very isolated.
By the time DS1 could walk at 11 months he was a different child. Still very quick to cry if something didn't go his way, very low threshold for frustration but he certainly wasn't crying 16 hours a day anymore! He's 6 now and really really fantastic. Just such a calm and 'easy' child. Has been since he became a toddler! Everyone else with placid, smiley babies seemed to hit terrible 2s just as we were getting to the good bit!
When I was pregnant with DS2 I remember thinking, well he can't be as bad as DS1 was as a baby...pah! My goodness, he was worse because even walking around with him in any position didn't work. He wouldn't sleep, he just cried for months.
Once again I was back and forth to the health visitors, got referred to paediatrician and even tried dairy free and reflux medication again but once again nothing changed.
Once he could crawl the endless crying diminished but he was still a moaner, basically would just whinge and whimper all day over nothing, no matter what I was doing or how much attention he was getting. Again, once he could walk and particularly once he could talk a bit, the whinging has stopped.
He's just turned 2 now and still very head strong and determined to be into everything his big brother is! But he is just so sweet and funny, really chatty and smiley. Comes running for cuddles and says 'I love you Mummy' 1000 times a day.
My advice would be to pester the doctors, pester the health visitors, whatever it takes to get someone to take you seriously. Make sure every avenue is explored. That way at least you feel like you're doing something and not feeling useless and frustrated. Above all else, know that it will stop. Whether it's frustration at being a baby or real discomfort, I promise you it will stop. You will survive this and one day you'll realise it was totally worth it.