5 year old can't play by herself

by Trista
(Canada)

I'm wondering what I have done wrong and if my daughter has sensory issues. She has never ever played alone. She seems aimless and bored unless I play with her and I am exhausted. She still flaps her arms in great excitement and opens her mouth when she does this.

She's having trouble at school with the noise levels although she is handling it externally, she is always telling me she can't handle the noise.

She can't stand sitting in one place at school when they have to sit for circle time but she does it anyway because she says she knows she has to but she complains and cries when she comes home.

She still has her soother after school because she seems to need it. One doctor recommended gum but she says it's not the same.

She's also having problems making friends. She holds back and doesn't really interact directly with the other children.

The two main issues are the not ever playing alone and never has been able to and the flapping. Could she have SPD? or is this something I have failed to do as her mother?
Who would I see about this?