Concern about baby' back and sitting milestone

Hi All,

My son is 5 1/2 months old and he is formula fed. Right from birth he spits up milk if proper body position not maintained. He always keeps his back rounded, while sleeping he used to make circles and used to sleep on sides. His head control is good, though with some lag and he can roll over too.
We have to mostly keep him on our shoulder. If we leave his body even a little free\loose, he woobles\shakes and he spits up. His back seems like a spring- unless you keep it fully supported and also straight, he spits up. We were never able to make him sit on any bouncer or stroller (can’t hold his trunk & slips down)

Looks like his back muscles\nerves didn’t get required stimulus or develop good. We are starting to now gradually make him lie on hard surface for few hrs per day. But I was wondering if any other tips or exercise etc we should be trying. Can doctor help with this ?

Thanks