Well, I battle with anxiety as an adult with an ASD, and I could write a few volumes on anxiety as a child with an ASD
It was interesting going to a recent lecture by a psychologist on anxiety and autism. The placed was filled from one end to the other with parents wanting to know that exact same set of answers: Almost no research has been done on anxiety in ASD but it's one of the huge, huge things. I read that something like 80% of us struggle with anxiety issues, unsurprisingly.
As I understand it, there's no dx for your son as yet, so you don't know what he might or might not have, but let's assume it's an ASD anyway just for the sake of something to talk about...
For us, the whole world is set up to work in ways we can't handle. We do one thing at a time, so we can either see, or hear, or walk, but not necessarily all three at once. We can look at someone's eyes, or listen. But not both. We can feel how uncomfortable our clothes are, and how hot the sun is, and hear how noisy the birds are, and smell how much perfume someone ten yards away is wearing...but be unable to switch any of it off. It's exhausting, and confusing, and often painful to have so much input all at once that just won't switch off.
Put us somewhere quiet and familiar with no socialisation required, and we're often totally happy. We can pace ourselves one thing at a time.
Put us in a noisy, bustling, indoor place with lots of people speaking at once, and we're shocked into silence or panicked into tantrums or fear.
As an adult, I've learned to control it better, but it doesn't go. I like to be places where I can cope, so I've designed my life to offer me those wherever possible.
But life isn't set up for us. It's hard. We really do need to work and think differently, and learn gradually how to cope with the social stuff and the sensory overloads that everyone else can cope with so much more easily.
Tips? Learn what the world is like through his eyes. Maybe find good books on the subject, or have a read of my ramblings on here called A Day In the Life of Amber or Another Day in the Life of Amber. Many wise words from others with an ASD too, like Bullet123.
Plan ahead so he knows exactly what to expect that day, and try to keep to it. Explain everything you can, in pictures if that's what he'd prefer.
Be patient with him, respect his need to withdraw or do something different if it helps him.
Good luck with the dx appointments too - when are they going to be, do you think?