That sounds really difficult. Is he verbal or using PECS or makaton or anything?
Most likely things will improve over time but unfortunately there are no easy fixes. A lack of communication can be a major factor as can sensory issues and just general maturity.
Have you been offered a place on an EarlyBird course or your LA’s equivalent?
Presumably he refuses a buggy on the school run too?
Reading some books on sensory processing issues may be useful. Understanding your child’s sensory signals and The out of sync child are good starters.
If he is not yet verbal or has some speech delay the Hanen More than words book is good.
General good books are How to raise a happy autistic child and Uniquely human.
YouTube is a great resource. Nurturing Neurodiversity and Vincentville both have boys around your ds’ age. Chirp and Walkie Talkie speech therapy are both US SALTs and have a good back catalogue of informative videos.
Do apply for DLA if you haven’t already. The Cerebra guide to completing the form will help.
Be kind to yourself and try to get some time to recharge as it will help you cope with the tricky times 