I’m completely lost!

The emotions after school situation, can sometimes be referred to as the ‘4 o’clock time-bomb’, because of the stress of masking/ camouflaging/ compensating all-day. It is very common for the behaviours between school and home to be polemic.    

The best solution sometimes can be the most simple one, to allow them to just vent the day away for a moment in their sanctuary, once they’ve release the pressure it should be better.  
I would say that what you are seeing is the product of acting-fine at school, your child feels comfortable enough to not act at your home, and that is a good because they has a place to defuse.

Ways to reduce that burden can be:    
To give them a safe place to be alone, to distract them with special interest (and not to urge them to revisit the overload), to listen to them when they want to vent (without offering remedy).

You know it’s that age! By the time they approach high school everything goes mad. It’s so common, but people put it down to hormones. Of course they play a part, but it’s the whole overload thing, and trying to fit in, and the possible sensory issues. It gets tough! And acting up once they get home is a classic sign. They’ve been trying to hold things in all day….

So yeah, an assessment seems a good idea. Schools can be rubbish when reporting issues, because they don’t see any, and ignore the subtle differences, especially if the school work is being completed well and on time. 

You are far from alone in this. We see similar situations every week on Pinpoint Cambridgeshire, which includes lots of parents both in Cambridgeshire and elsewhere, even some from overseas. It is a charity run by volunteers to bring together parents of Autistic and ADHD school age children. See www.pinpoint-cambs.org.uk/.../

Sorry this sounds difficult! And being a single parent is not easy, I know.

There are a few fundamental specifics with the Autistic-neural wiring which then express in many different ways. 1. Difficulty with language - accessing vocabulary and this includes finding the word or identification for a thing. What can often happen is while we can internally reason through an idea or an exchange or any thought with images (like a silent movie) and calculate outcomes or probabilities, we might not be able to translate that into words. We might even have too many things or parts of a thing to express all at once but our ability to talk about it is a much slower process than the ability to think about or visualise it. I sometimes describe my brain like a really messy library. Books aren't in the right location, when I ask for help on a topic, several librarians arrive with carts overflowing with material on the subject and I don't know where to begin. When I was young I'd just break down in to a puddle of tears.

I really needed quite a different structure of education than I received. for instance, when I took a Logic class in Uni, I was 17 and it was life-changing. It took a while to turn these formulas into a 'second nature', but it helped me follow and focus better and know what I was looking for when learning and listening or reading.  Another thing that helped was theatre class, music and art for matters of expression when words don't work.

Stress adds to this. I'm in my late 40's and find when frustrated and stressed I still have difficulty accessing the word I need though I worked incredibly hard throughout my 30s and continue to expand my vocabulary. Newspaper columnists are incredibly helpful. But I still use a placard to read and I read slow, but I love reading. Theatre classes actually helped with this too, as we'd say a sentence and then imagine it. This task is slow to begin. But as you get older, it has turned a natural inclination of my imagination into a talent. 

This brings me to another fundamental difference. 2. We don't cannot dull our senses and this is often referred to as being hyper-sensory. Autistic children sense-perceive beyond their years and well beyond their wisdom. Not just sounds and smells but also the physics of things and seemingly invisible systems between people. But without the science to interpret what's happening. Now I'm older I can easily tell the difference between an LED and a halogen if we were in a dark room and you were turning them on and off at random. And now I can also explain the science behind why the LED hurts and the halogen doesn't, which can easily be stated in one is unnatural and the other is a tiny but natural source of light - emanating just like our sun. The best thing for this is to always encourage learning: be curious, exhaust problems, make room for even more answers. Awe. And stick with natural elements as best you can: natural fibres, no added chemicals, non-scented products, etc.

There is a 3rd which is important. 3. Monotropism: https://monotropism.org/ It explains much of what it means to have an Autistic brain. Hopefully these can help! 

And know that sometimes pushed to tears can actually be a relief. It's not a preference but one needs to be able to get it out as most likely the stress will rebuild tomorrow. Society is not built for us. But it needs us. I hope you can find some time to destress yourself.