Feeding rabbits alfalfa

I have a rabbit who's allergic to hay. I've been to the vet with him and he's getting atarax and cortisone (to inhale). Recently I tried giving him and his partner alfalfa instead. He's still reacting to it and breathing fast, but he's eating and drinking a lot better and is moving around more. I'm going to try feeding him oxbow Timothy hay, maybe it's just the brand that has made a difference, but if it is the alfalfa that he's less allergic to I would like to keep feeding them that. However, from what I've read, alfalfa isn't good to feed rabbits long term. I will talk to my vet about it, they're really good with rabbits, but until then I would just like to know your opinion on if alfalfa is ok to feed them long term. What are the risks?