I’ve never had experience with pinworms, but I just checked Lucile Moore’s book, A House Rabbit Primer, to see what she says about them. She says they are very common in rabbits and may be difficult to prevent even with good sanitation. They are transmitted through ingestion of contaminated food and water. Spores are shed in the urine and can remain viable for months. She also says that pinworms rarely cause a rabbit problems and they are often not treated unless it’s upsetting to the owner. The treatment for them is to use a parasiticide such as fenbedazole or oxyfenbendazole. Or, adding piperazine citrate to the rabbit’s water can be effective.
It seems strange that your other rabbits don’t have pinworms, since I assume they would be eating and drinking the same thing as the rabbit that does have pinworms. Or they might have picked them up by sharing a litter box, if they do share one, so I do wonder why they also don’t have pinworms.
Is your rabbit excessively grooming her anal region? If not, the pinworms may not be bothersome to her, so maybe you could forego using a de-wormer since she had a bad reaction.
One of my past rabbits, that I found on the street, had tapeworms. She was given an injection of Droncit. That was a while ago, and I’m not sure that is still the treatment. Is your vet sure that these are pinworms?