I'd love a co-sleeper...
You can remove the side off any, normal cot bed. They are designed for the sides to be removable and the whole thing still be stable. You just only remove one side, not both.
Therefore you can do it with his cot now, if you liked. I'd move furniture (bedside tables, drawers, dressing table) out of my room to fit the cot next to my bed, if I needed to.
I suspect moving an already poor sleeper out of the cot bars and into a toddler bed will create far more problems than it solves.
But if you want to go this route I'd suggest setting up some form of perminant floor bed for parent and child to sleep on in his room. It will end up being no different to cosleeping, just in a less comfortable bed than your own bed.
last night he calmed down when I was holding him quite tightly. Would swaddling him be bad at his age?
That's interesting. Was he swaddled as a newborn?
It's not unusual to need to still and calm baby. To effectively have to pin them down (gently, of course) to help them learn to be still to go to sleep. Especially when learning all the mobility skills (crawling, standing, walking), it's like baby didn't know how to stop and calm in order to sleep.
Maybe a tightly tucked in blanket will help? Putting a sheet across-ways (rather than lengthways) to tuck all the way under the mattress so it's very tight and snug.
Firm hands on him is good for this too. It provides reassurance that you are close, while also encouraging stillness.