Was he completely normal yesterday? Did this just happen suddenly? If this was sudden, it may be a prolapse of the esophagus.
Let's assess this. With this "thing" filling his mouth, he can't eat or drink. Not being able to eat and drink are basic to life. He will die unless he can eat and drink. 
Therefore, you need to open his beak as wide as you can, and if it hurts him, that will just need to happen in order to try to help him.
If this is a prolapse of the esophagus, then you may be able to push it back down his throat. If you aren't willing to try to do this, you cannot help your rooster and he will die. If you want to save your rooster's life, you will need to have courage to try this. 
You have no vet to do this for your rooster, so you are it. Time to be brave so you can try to help your rooster.