Unsure of the next step

Hi, I'm wondering if anyone has any advice for our current situation 

I have had concerns over my 6yr old daughter and some of her behaviour and things for a few years but everytime I bought anything up I was dismissed as over reacting.

Some of her behaviours include: an intense rain and wind phobia, waking up at night scared if she thought it was going to rain the next day, sobbing if it did rain etc.

She hates certain noises, if her 18month sister cries, she cries too because she says it's too loud, will jump at the smallest noise such as hearing next door through the wall. She will often put her ear defenders on as she says things are too loud.

Intense tantrums over what appears to be smallest thing or if asked to do every day things such as brushing her teeth or putting on shoes. She will immediately cry, scream, try to hide under the table, kicking and hitting and physically lashing out. She often trys to bargain to get out of doing these things as well

She needs her routine to stay the same, any change causes intense screaming and crying as above.

If she spills anything she cries and if spilt on herself she will immediately try to strip, even if it's a tiny amount

She seems to struggle with understanding other peoples personal space but is very protective of her own.

Towards the end of yr 1 after thinking she had been unlucky with bugs the doctor told us her sickness was down to anxiety, he asked us to do a behaviour diary for a month and at the end of summer referred her to our community paediatrics team, but they returned the referral saying she was showing normal behaviour??

However last weekend completely out of the blue she told me she wanted to die because she was awful and stupid and always got things wrong. When asked who said that she said 'I do, I always get things wrong'. This was said very calmly.

I have since spoken to the school and GP, I have an appt with her teacher and learning mentor tomorrow and the GP wants to see her next week after a weeks mood diary. I asked about a referral as was obviously concerned but was told to wait for a face to face appt

The school have said they see nothing at school apart from her being a little anxious at  times and is a bit of a perfectionist but her headmaster says it is possible for children to mask it very well at school.

After a routine appt for myself with a nurse this morning it was her who suggested that my daughter have a form of autism and to push to get answers for her but I dont know who to push.

I want the GP to refer her again but is Camhs the better people to be referred to whilst also just seeing if I get any further information from the school to help.

Is there any specific questions i could or should be asking the Dr or school to help with it all?

Thank you for reading, I've just realised how long this has become x