I'm not a teacher either but a parent of a figity, difficult for School, could have a dx of ADHD if we want it, aspergers traits, dsypraxic traits 6 yr old now in yr 2 - yr 1 was terrible - I think its a complete change from the play based learning in reception and there are lots of children who struggle with the transition.
Firstly I would be asking what school are doing, what is the TA's background/experience/age/qualifications? does he have an IEP? How is he being helped with turn taking and socialising? I'm not sure if you should wait for a 'label'/diagnosis (if thats what you want) if you recognise behaviours then ask School to specifically target those behaviours (which hopefully they are with the TA) Who has he been assessed by? another teacher or an expert? Ed Psych? If you have IEP's then you can review their action plan and your ds's targets. Its also good to have an incident log - when is he removed from class? what happened? what was the trigger? is there a pattern ie always just before lunch or during a certain class?
The Ed Psych could be important for understanding the behaviour - we had an ability assessment through school last year, he also identified that sticker charts DO NOT work for our ds (we did say this to School before but they needed to hear it from an expert) They have a negative effect to his behaviour, he views it as manipulation and the whole week was on display - why on a Thursday would you want to know you had a terrible day on Monday?? He labelled himself as naughty and psych said his self esteem was cronically low and advised us to find him an extra curicular activity to raise it - Beaver Scouts has been amazing for him.
You also mentioned the doctors - was there anything for him to do whilst at the doctors? my ds will play with bed or stethascope etc if there is nothing to do, talking is boring, I take some books with us now - its working out what works for him - you could have taken a computer games and I'm sure he would have sat beautifully but that wouldn't mean he was or wasn't ADHD...
I'm not saying your ds is or isn't ADHD but I totally get how upsetting it is to constantly hear what your ds CAN'T do - you feel like you have failed somewhere because it seems like everyone else can do it. Your ds is still young, school doesn't suit everyone and it is very reading writing based. I also think once someone gets under your skin as difficult its difficult to see the positives (I see this at work all the time!) I think this happened at School last year with ds, his teachers this year are amazing and he is starting to settle down - he is allowed to have a bad day now if that makes sense.
We've done loads on diet and routine - strict bedtime routine so can wind down, multi vit, omega oils (if chewable check for additives),reduced sugar (no squash, limit sweets) some compliementary therapies too, It might be worth posting is Special needs as there are lots of people who have experience of different types of behaviour and dealing with school who can help x