You are doing the right things. My own DS went through something similar when he started school. He was a bright, outgoing, happy toddler and well settled at nursery who saw no problems at all (well he a was a bit tantrummy and liked his routine but so are many toddlers, and the nursery workers who knew him from a baby could calm him down easily enough) until he started school and then all hell broke loose.
Getting a referral is a good idea. For my DS it turned out to be an ASC, DS couldn't cope with the new setting and new demands. Luckily we didn't get much shit from other parents, I think the school were very good at intervening and protecting the other kids, and the teacher had taught a simlar child before and knew the kind of things that would help to keep DS calm although things didn't really improve until DS was diagnosed and the school put extra support in place because he did need one to one.
You are not a crap parent. There is a limit to what you can do at home - I couldn't discipline effectively at home for what happened in school, and the school rarely asked me to because it just made DS more unahppy and anxious and aggressive in school. DS behaved well at home because home just didn't have the same triggers - noise, bustle, lots of other kids, unstructured play with less supervision tha nursery, etc.
While waiting for the referral I got good support from the HV and also from a parenting group. I was the only parent of a child awaiting assessment but the group leader was really understanding about how hard it is to discipline when you don't really know what is causing a child's behaviour - it is unfair trying to reward or punish if they can't help it or can't understand cause and effect, and until DS was assessed we didn't know what he could and couldn't do. The group leader supported me to keep things consistent, calm and friendly at home. I found that "if in doubt, treat it as a can't not a wont" worked very well.
It was a horrible time though. Things only really started to get better after DS's diagnosis and when he started getting support.
