Is my daughter autistic

My daughter is 16 and struggles both emotionally and socially. Although she is high functioning, her awkwardness, that I once thought was part of her character now seems unusual compared with other teenagers of her age. Could she be autistic? I have listed her symptoms below.
-  E has a resentment of any physical contact . Since birth she has hated having her hair and teeth brushed, nails cut and any soap, shampoos or cream being applied. This has resulted in screaming uncontrollably..  Although E has learnt to tolerate some of the necessary daily hygiene routines, she still has a strong dislike to water going over her face. Therefore I am still washing her hair and have to have a towel at hand every time a drop of water goes near her eyes. She has also never kissed me and won’t accept a hug unless on her terms.

- E has no sense of smell. Something she has been medically examined for and couldn’t find any reason for.

-  She only eats certain textures of foods with no spices and finds it traumatic if anyone tries to persuade her to eat something she doesn’t want to. As an baby she refused milk , by the time she had nearly finished a bottle it was time for her next one. This continued with solids. E would store food in her mouth like a hamster and then would spit it out at the end of feeding. Her diet, until the age of 10 was very limited and at one point she only ate plain pasta and fruit.

- E can hear conversations in the background from a distance and struggles if too much noise.

- she is sensitive to lighting and cannot focus on any details if the background is bright.

- E struggles to form and maintain friendships. She sometimes doesn’t understand the rules of friendship and finds it easier to make friends with girls a couple of years younger than her. She copes better one to one or in small groups.

- She doesn’t show the same empathy as others. For example when I was once ill I called an ambulance. E woke her brother as requested by me to let the paramedics in, she didn’t ask if I was ok, nor show any concern. She said excuse me to the paramedics so she could get her school top and waved goodbye to me when I was in the ambulance and went to school. E can’t understand others feelings and focuses solely on her own.

- E has anxiety, especially when dealing with social  and things she needs to complete.  As a child she found it impossible to speak to adults , resulting in some people thinking she was ignorant.

- Her thinking is black or white, there is no reasoning or compromise.

- She has extreme meltdowns over things that may seem stupid to others. They go from 0-10 in a matter of seconds and it’s difficult to calm her down or reason with her.

- E often questions what is wrong with her, why doesn’t she fit in and what is the point of her being here.

- She struggles with change of routine and transition. E has struggled with this throughout her schooling. She has been reluctant to give up childhood routines at home such as tucking her in at night and still often requests this.

• E becomes obsessive about things she is interested in and has to know everything about it. She is highly attached to certain objects.
• She gets highly upset if things don’t go her way.
• She can talk continuously about her interests and doesn’t realise if someone is becoming bored listening. E finds difficulty in listening to and responding to others when they talk about their interests.
• E can often respond to people using inappropriate words (not swearing, but words that can be hurtful) without realising what she has said and the impact it has on others. Her speech is more ‘well spoken’ than her peers.
• E had difficulty in some sports and activities such as learning to swimming and riding a bike. She can sometimes be rigid, or stiff in other movements.
• By the age of 3 E knew all colours and shapes up to an octagon, showing a high intelligence in mathematics. However, she continues to find English difficult and has been diagnosed as dyslexic.
• She has a very low level of tolerance to pain and regularly complains of joint pain, headaches, sore throat and stomach pain. E often has constipation.
• Her need to for me to be constantly at her side whenever she wants me is overwhelming and she cannot understand if I can’t be there for her for any reason, including work commitments.