We took him to the vet and it turns out I was all off and it was his shoulder. Go us. The vet gave us anti-inflammatories and told us to come back in a few days if that didn't take care of the problem : it's either a stretched ligament, either a rare growing disease, so we're hoping for the stretched ligament wich should be getting better with the pills. The disease is not fatal, it just means there's a bone bit bothering him and an operation would be necessary, so still not fun.

Thanks to everyone for the advice! If he does hurt his paw pads, I will know exactly what to do.