Any of you have stuttering children?

Any of you have stuttering children? My 3 year old has, in just a couple of weeks, developed a really really bad stutter. We are taking him to a speech therapist but the wait for an appointment is really long. In the meantime I don't know what to do. I've been reading online a lot and have changed the way I interact with him ( eye contact, letting him finish, not correcting him, and generally speaking in a calm and relaxed way with him ). It breaks my heart to see him struggle to get a word out. It's almost always the first word of his sentence. After a while he gives up and whispers the sentence which usually goes much better but I feel so helpless. I want to help him. Please do you have any tips? Thanks in advance for your advice.