Is your vet experienced with dentals in rabbits? To me it sounds like they are not? If you can, I suggest finding a specialist or at least getting a second opinion from a rabbit vet. I had a rabbit with rotten molars and they were removed (he was also very young, it really sounds a lot like your bunny’s case). If they aren’t it could lead to abscesses. As long as not all of his teeth are removed, he will still be able to chew.
If the teeth are not treated, things will likely get worse, and it’s unlikely you could manage things with just antiobiotics and pain meds.
I also suggest talking to the shelter. Sometimes when problems occur very soon after adoption they can help you with medical costs.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.