I don't know what to do

Hi everyone. I joined in the hope someone might know what this seems like. I have a girl who is 4 years old and 9 months. I also have a just turned two year old. Since my son was born my daughter seems to of gone through alot of different things that have left me confused. I never know whether it's the affect of a new sibling or something more.

She reached all her milestones and was as easy content baby. She talked well from 18 months. 

When her brother was born she was 2 years and 10 months old. She started going mute when we left the house. It came out of nowhere as she used to talk and sing alot. After two months she unmuted and went back to speaking to me and her dad, also my friend and her son who's the same age as my daughter. Unfortunately she still doesn't speak to her grandparents and aunties for hours and it has been really difficult trying to get them to understand. 

She started school in September and was shy and always on the art table. The first parents evening the teacher said she was gorgeous and so good but taking ages to pick up the routine. She wasn't massively mixing. I spoke to other mums who were told their kids were not massively mixing either. They also mentioned her cutting skills etc but we've improved on that! A month ago I was called to one side. She was now being too lively and not listening. She hit a boy once! I solved all this by a Tele ban for the weekend. The following week the teacher said she was good again but still hadn't got the routine yet and was needing lots of reminders still. They want me to get her ears and eyes tested as her concentration is not great and she doesn't always grasp what she should be doing. 

Reasons I'm concerned are...

The refusing to speak to family.

Won't say hello or good morning to anyone really. Never said hello or greeted nursery staff either. Won't answer strangers or thank people other than me and her dad. 

Walks past the teachers when they say morning and avoids eye contact (other than that she speaks to her teachers)

Won't let me touch or hold babies without getting angry and anxious 

 Between ages 3- 4.5 most playdates were frustrating and never went smoothly. Teasing her friend (she's best friends with this friend now and they are together at school always) not good at sharing. Hated my friends child who's now two. She felt constantly threatened by this two year old and would go crazy if I helped her. I can't invite her friends over as she's so anxious about me talking to them or helping them.

No interest in mothering or being kind to younger children (only her brother) she will say babies are cute etc but doesn't want me to fuss them

She went through a fear of public toilets. I can get her to use them now but hand dryers freak her out.

Shes  so messy! damages things so easily. Books get ripped. Games get tipped out the box and no longer can be used as pieces go missing. She draws on things. She takes dvd covers out the cases. Throws paper and all-sorts everywhere. Pinches my jewellery. I got some paper cups yesterday for Christmas parties and she started drawing on them. She never looks after her pens and leaves the lids off. She chucks stuff allover and I can't keep up with her mess. I'm concerned that she doesn't appreciate the value of things and doesn't respect what's not hers to touch.

I'm worried she isn't twigging on at school as easily as the others. She needs constant reminders from what the teachers say. 

She goes through stages of being obsessed over one thing. So for ages now she has been drawing. She draws everyday but gets through tons of paper and pens and chucks it everywhere. In the summer she was playing with a blanket up her top for weeks. She was pretending she was pregnant. She went through a stage of filling bags up with random things and food. She's now obsessed with her hair. She wants plaits and it super long. She spends a chunk of the day brushing it. 

I guess the reason I'm writing this is because I feel she is so anxious in social situations (especially if I'm around) I often feel we all miss out due to her being like this. I can't hold babies. We can't go to people's houses with babies. We can't have people here. Going to the park is. Disaster as she just winds up friends. We haven't done this for four months though as she's at school now. She's also going through a stage where she keeps telling her dad to stop breathing. It's weird and driving us mad and he's not noisy with it. She gets so angry about it. 

Mostly she seems ok. She's average with her reading and writing. Starting to write some letters and numbers. She's recognising much more when she's reading but certainly not amazing yet at it. She seems to play with a couple of different kids now. She doesn't like other kids walking home from school with us (apart from my friend and her son) due to her not wanting to share her friend. She doesn't have any problems with eye contact and does understand things. She responds to her name etc. She does take things literally but is that her age? She can be really funny and silly. She also can have days where she is an absolute star. She is improving slowly with her confidence. She role plays the teacher alot at home and sets up her own classroom and talks to herself. She also plays with her brother. She loves being outside too. 

Does anyone think she needs to be seen by a Dr? Or does this sound like anxiety? I feel like she may have Asperger's but then when I do online tests she never scores enough to have autism. Thanks for reading. Please share any thoughts