The best thing to do would be to take him to the vet. However, I have been in the situation where my dog had a minor injury and I treated it at home. I am not a vet or a tech, so my advice might not be right, it's just what I have done. It sucks that vet care is so expensive. If there is any inkling in your mind that there might be something stuck in there (splinter, bullet), take him to the vet!
Is it on the front of his neck or the back? My dog was playing in the park with another dog, and the other dog pushed Samson into a bush. A branch went into his neck near the collarbone, making a roundish, about inch long hole. I took him to the vet b/c it would not stop bleeding, where they gave him a few stiches. It cost a lot b/c he is a larger dog (anesthesia is quite a lot for him!).
If the dog is not letting you look at it... is he nipping at you in pain? If it's that painful, I would just take the animal to the vet and try to work out some sort of payment plan. Is it gaping open and bleeding a lot or just a little open and oozing? Bleeding more than a little that you cannot stop needs medical attention.
If he was just pulling away, I would take a look. First, try to trim away as much hair from the area as you can. This will help it to heal and also the hair will not get in the wound and irritate it. Wash it. If you can try to irrigate it, that would be best. Put some neosporin on it and if you can bandage it. I HTH.
I have a book called "The Dog Repair Book" that has come in very handy