Try and get a paediatrics appointment booked and book a meeting with his teacher/ head of year and ask for senco to be present. Write down what leads you to believe this as in his actions etc and go from there. Show the school you would like to work together. However diagnoses for kids can take years!
Maybe you can express some concerns to the school and ask them to refer him
Whilst your intentions are admirable, you're unlikely to be able to do anything with PR. If he's excluded then I'd hope your mum will take things more seriously.
I'd contact the school and see if there's any support they can provide? Being excluded seems very extreme specially if they haven't provided support or an alternative? Unless they have and your mum's ignored it?
This is just my suggestions are you able to phone the GP and take him instead and see if you can get an appointment and also a sit down meeting with his school expressing your concerns and worries and explain how he is at home and at school and see if they could work with you and try get him the support he needs as he is still a bubba and it’s hard to regulate emotions regardless definitely at that age x