The current and prominent issue that has to be addressed is constipation. You need to approach with right homoeopathic medicines and following tips. As you can see there must be digestive issue you are providing diet , high roughage, low refined flour and plenty of fluid s the problem he is facing is dyschasia where a person avoids passing motion owing to pain that might have occurred in past which trigger anxiety and fear of passing stool
Next Steps
As far as his autism and anxiety issues are concerned your are very much rightly feeling to start homoeopathy which is the only and best option to deal with it which can also improve his behavioural ,emotional and symptoms of autism to good extent
Health Tips
1. give castor oil with milk daily so that it soften s stool and passes easily and encourage him to pass daily at fix time .