Has you kitty been to a vet recently? You say there is no ER vet that will take him- is it because of the holiday or that you might not have the money?
Ok, very gently open his mouth and see if he has an obstruction. Because he is so young, you need help with this, or you will get bit. Someone needs to hold him in a towel and try first just using a small flashlight to see if you can see anything? My guess would be kitty found string? or a rubber band lying on the floor.
Is kitty pawing his throat or making motions with his paws to the sides of his mouth? What color are his gums? Are they pink and happy or pale or grey?
If there is an obstruction that you can see, removing it by yourself is not advised because if you say, take your little finger and try to push it down- depending on what it is, you could effectively block off the cat's airway. SO DON'T DO THIS!!!! Don't remove it by trying to push it down. I am just trying to help you understand how severe this might be.
If you can see something and honestly this situation NEEDS a vet. The blockage has to come up and not down. It could be anything, a sewing needle, anything the kitty found on the floor to play with. Kitty could also have gotten into something like cleaning agents, found a pill on the floor that someone dropped.
This is again, something that a VET needs to address. This is the best I can do. Cats purr when they are in pain and the "rumble" that you talk about is also a pain sign. Your kitty sounds very ill and needs to see a VET. Please call a vet, or an animal shelter, call the poison control center, call someone who can address this problem in the here and now and not over the internet. Good luck I will be praying for your kitten.