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Hello. I'm sorry to hear about your dog.
If you can't get in for x-rays, then the next best thing you can do is clean up the entry or exit wounds to help prevent infections. If an organ was hit, especially the intestine, there is nothing you can do to prevent the inevitable. As long as it's just flesh wounds, he may do ok with just local care.
I would use some electric clippers to clip/ clean each hole that you find. You can use warm water/ soap solution to clean them. You can then rinse with saline. I would also use a triple antibiotic ointment like Neosporin on them to help them heal faster.
You don't need to try to remove any bullets, as they don't cause any issues under the skin.
I hope this helps, let me know if you have any other questions.