How can I ease a sore throat with something that won't irritate reflux?

Dpends on cause. It depends on what is causing the sore throat.If the sore throat is caused by streptocaccal bacteria, then you need to be treated with antibiotics.If it is due to a viral infection etc, then you can such on over the counter sore throat lozences like cepacol or others, or just gargle with salt and warm water for symptomatic relief with/without over the counter pain med like acetaminophen(tylenol).