The diagnostic process is very long sadly, so my advice is to start keeping notes and a diary. Make notes of when he finds things difficult, what they are, how they affect him.
In terms of supporting him, also keep a note of when he is upset about something (like the issues you've listed above), how he reacts, and what precipitated the upset or meltdown. You'll start to get a feel for what you can usefully avoid and then work on finding solutions to the things that you can't avoid.
You need to ask the school for support ASAP, as they don't need a diagnosis to support him. Also, go to your local authority website and look up 'Local Offer' (daft name, but there we are!). It will list everything you need to know about supporting children with SEN or disabilities (diagnosed or not yet) in your area.
You will also have a local parent partnership forum (funded by a charity called Contact) as every area has one. Not sure what it will be called (they vary) but all local parents in your area with similar issues and/or SEN kids will be there and they will usually have a secret FB page and forum where you can chat to local parents in the same position as you. They are incredibly helpful.
Go and see your GP to record your concerns, ask your school what they can do to help/support and start to keep a fiel for al letters, emails, appointments etc.
Keep your diary up to date, as you will be filling out endless referral forms along the way so the more information you have, about your sons day-to-day struggles, the better.
And lastly, a huge hug. It will be okay. You are not alone in this, and the community you find because of this will not only help and support, but literaly keep you sane. You and your son sound awesome - believe me, if I can do this (I'm ASD/ADHD as are both my kids and I'm a lone parent), anyone can. And yes, get yourself to the SEN boards here! Have one of these
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