This!!! The baby is hungry and unsettled and needs more milk.
My two DC were so different. Firstborn very similar to what you've just described. Very clingy and unsettled and I remember clearly feeling all the emotions you have described in your post, OP.
He was a small baby, I was inexperienced at breastfeeding of course and he had trouble gaining weight. I was determined to stick at it and I didn't understand the cycle. He would only fall asleep when he was feeding and I would let him because it was the only break I got as he wasn't sleeping well at night. So he wasn't getting enough milk as he was snoozing rather than feeding and that led to unsettled behaviour, bad sleep, and me being exhausted and emotionally frazzled as I never got a break. I had recurring bouts of thrush on the breast due to not latching him on properly so feeding could be agonising and I was utterly exhausted. I felt trapped and miserable, reduced to a sleepless milking machine.
Things only changed when I began to combi feed. I only did this as we were not allowed to be discharged from midwife care due to his only gaining very little weight. As soon as I got over the mental barrier of using formula, life got so much better. I no longer felt the fear every time he cried. It took pressure off if I was sore from thrush and gave me a break. I could have a shower on my own or eat my dinner as husband could bottle feed. And my DS gained weight and so began to sleep better and be generally more settled.
I heard so many all or nothing horror stories from midwives about how if I started to use formula my own milk supply would drop, the baby would get 'nipple confusion' and not be able to breastfeed any longer etc. That was all absolute bollocks. They wouldn't supply any detail on combi feeding so I turned to the internet.
I continued to feed him myself and also give the occasional supplementary bottle. In time,I ditched the bottle feeds and returned to exclusive breastfeeding when things had stabilised.
With my second born DD, it was so different. From birth I woke her up every three hours for a feed, something I hadn't dared to do with DS. I made sure she was latched properly and she was awake during the whole feed. She took in a good amount of milk, and that meant she slept longer during naps and at night. I was better rested because she was more content and could be put down and I had just that little bit more freedom and rest that I felt much more sane.
I had a couple of the ready made formula bottles in the cupboard ready to go, just to take the psychological pressure off, but never needed them!
My point is it really is all connected-feeding/ sleep/your own emotional state. You have to do what's right for you and your son, but just be aware that you have options, it doesn't have to be all bottle or all breast.
Newborn babies are programmed to eat constantly and gain weight, so everything comes from that. If they're not getting enough milk and are hungry, everything else falls apart.