The stuff your describing with the feeding sounds awful
. It could be something medical like reflux, or an intolerance, and their is an awful lot to be said for your instincts about whether there is a problem that needs further investigating.
However, it could also be something more straightforward and easy to fix to do with feeding. For example, oversupply might cause these sorts of issues, as baby might be getting lots of the more watery milk produced first, this is lactose rich and can lead to lots of digestive issues. It can also make them unsettled, as not only is their tummy uncomfy, but also they don't feel as full because they never get to the richer fattier milk because their little tummy is full already, but it's not as calorific, so they get hungry, and the cycle continues. This would make sense in conjunction with a fast let down, or less than perfect attachment, leading to lots of fussing at the breast. There are other possibilities too, for example various possibilities linked to tongue tie or even tongue tie after division (which I think you mentioned?).
It could be lots of things. Can I suggest you ring one of the breastfeeding helplines and start by talking through the feeding thoroughly with them? They are great at listening and will really hear you out. If it does turn out to be something like reflux, then they will also support you with any breastfeeding aspects whilst you get the medical care you need from a doctor. The BfN are on 0300 100 0210 from 930am-930pm, and there are other helplines too, I just don't have the numbers handy!
One final thought, sometimes, later and in restrospect, parents say they can see that these early issues were related to their child's personality and it's part of what it is to be them. You'll find our own way through, but many parents say that movement and carrying their baby close can help, a a good sling can be a real help.
I hope things improve very soon.