3 year old - not diagnosed, but battling

Hello everyone!

Feeling very happy to have come across some type of community during this strange grim time in London! This is my first post, so thought I would introduce myself. 

I'm a kiwi mother, currently living in Wimbledon, London, with my husband and three and a half year old boy. He's my first born and currently my only child (hope to have more in the future!).

I've suspected my son had autism since about his first birthday. He never had a real attachment to me, never cried when dropped at the childminders from six months, but I was blamed myself for that and going back to work too soon. Fast forward, and he will be four in May and I am still don't have a formal diagnosis.. huge gaps between pediatrician appointments and the doctor seems to think he needs to tick more boxes... and I feel his signs he has are pretty clear? 

He is a very active little man, loves climbing, running, jumping, water play. My son is extremely sensory, biting us all a lot, strangers, other children, teachers, and always putting things in his mouth, trying to eat things like chipped paint from the walls, stones, chalk etc. Which gives me anxiety!! He stims occassionally by flapping his arms, and sometimes likes to rock, but mildly. He has had a few pop out words here and there, but they last a week then seem to disappear, despite him being very noisy with screaming and other strange babbling sounds. He walks on his toes, LOVES the ipad, and any form of screen time (he can't go to bed at the moment with an ipad). Eye contact is getting better, but its fleeting, and not focused for long at all. I also have to work so hard to get him to show emotion or smile most of the time. He's not too bothered by change in routine, but if he doesn't get his way... ie. He wants to go for a bike ride now, or he wants his dinner now, he will have a complete melt down. I've started being too scared to take him to the park / playground because if he doesn't want to go home, he literally won't get back in the pram and will fully melt down in the mud on the grass...

From what you read, would you agree with me that my son might be autistic? and if so, what would you advise from here? should we push harder for a diagnosis?

We have a draft EHCP plan, but recently missed out of the space in the specialist nursery we want to send him to. So it sounds like our nursery should get some funding so he can have one to one support - as they have really struggling with his needs recently. I really don't know what to do / what is best. 

I'd really love to hear from other mums going through something similar, as sometimes it feels like a pretty lonely path. And if anyone out there has any advice on the education / diagnosis front would be sooo appreciated.

I'm based in Wimbledon, so if anyone is close by do also give me a wave!

Thanks Haley.