Her behaviour sounds very much like my own DC's (in year 4 though)
I've found the acting out with mine has been down to control - or feeling out of control - and needing the safety of lots of boundaries. Not saying you don't have them in place. But some SEN kids need stronger, black and white rules to feel less anxious.
Primary she would've had her own peg, her own drawer, her own desk etc in secondary you are expected to move between classes, no real 'space' that is your own and many transitions through out the day.
Mine behaves in school but takes out all the anxiety and frustrations with me at home (single parent too) and its taken 2 years of constantly hassling to school for help and buying my own interventions after school promised to fund them - weighted and sensory therapy, fiddle toys etc.
things I would do.
- keep a diary of all behaviours and moods, suspected triggers, sleep routine etc. This will help enormously when you finally see camhs. Its your evidence and a way to jog your memory.
-go back to your GP and find out if, in the meantime, they will help support you with implementing some measures in school until camhs can take over.
-find out in school if your DD can have a 'safe space' somewhere quiet she can retreat to of a lunch/break time when everything gets pretty hectic. Just eating her lunch away from the noisy canteen could really be beneficial. The school SENCO and GP can help with this. This can also help if she is the victim of bullying during these times.
- find out if anything is bothering your daughter at all. See if you can arrange a meeting with some feedback from her teachers if poss to see if a particular subject is the problem (my DC is worse on days English is taught. Better on maths days iyswim)
Kicking off in class, being disruptive etc can hint at a problem in school with learning, bullying etc. Being bollocked for her behaviour in school can lead to home outbursts as a way of pre-empting the telling off. Starting a fight is easier to manage than an unexpected one.
plus she's 13. She's probably dealing with body confidence issues, puberty, hormones racing, new school environment on top of the additional needs. Her head is probably in one hell of a mess and anger is the only way she can deal with any of it until she gets support.
at home remain calm, walk away from her rages if she is safe. If she breaks her property don't replace it. Don't even try to engage with her mid rage wait until she's calm.
A friend told me that often kids need a safe place to vent, to yell and scream and most often the safest way to do that is to our parents because no matter how much they call us an arsehole, tell us they hate us, we will still be there.