Switching companions help you a lot whether you are in the campaign,Hunting, or just doing site activities (gauntlet, seasonal events, etc. especially hunting, as in some guides a certain wolf & companion pair helps the success rate!)
You should be able to switch you companions anytime you want! Though, When you have recently played with your companions, it doesn't let you.(assuming you used nana to play with them all)
You should be able to after their cooldown ends though! I'm not much of an expert, and there may be other reasons why it happened, but this is what i know! :D
Just as a heads-up; the Questions & Help forum is the place to go when you have questions you'd like answered. Game Guides is more for written guides.
As for switching out companions. When you are on your wolf's profile page, there should be a small pencil in the top right corner of the companion block. (The same one you use to assign a companion to a wolf) Click it and a menu will pop up that let's you either remove the companion or switch it out for another one).
However, you cannot switch out a companion while it is on its cooldown. It doesn't matter if you played with it manually or through Nana - when a companion is on cooldown, it cannot be switched out. You'll have to wait for the timer to count down to 0