Need more info. What kind of specialist? ER referring her means it isn't considered an emergency.

Call the specialist and ask to be called if they have a cancellation and she should be ready to head there at a moment's notice, so hopefully she lives close. Has she called other specialists of that kind on the plan? Since it is an issue keeping food down, it's either ENT or GI - and neither of those are super uncommon, so she should call every single one on her plan and then get her GP to write a referral to whoever has the soonest appointment.