It really is a spectrum though and no child will have everything on the list.
Your dd sounds very similar to mine in many ways. Personality wise my dd is quite sensitive and tends to be very dramatic. She feels things very strongly and struggles to find a middle ground.
The play therapist talked to us a lot about 'sensory diet' and taught us some activities to do with dd to help her regulate her senses.
Does your dd have any self soothing actions? Dd had a soother til she was nearly 7 as she could not shut down to sleep without it. She also lives to rub her own and her dad's ears.
Dds issues are somewhat under control now but flare up in times if stress or anxiety.
I have tried to develop a thicker skin because I used to feel everyone was judging me about dd's open coat, no socks, scruffy outfits etc but the more open I have been with people the more I realise everyone had their own stuff going on. I've now met so many people who admit they have a child with these sorts of issues.
I'm not in the UK so can't really advise on where you could go for help. I think Occupational Therapy may be a good starting point. We found Play Therapy helpful but I am not sure what age group it is aimed at.
I'm not sure a GP will be much help, ours wasn't but could be worth a try.
My main advice would be to try and manage things rather than try to control it. You know your dd best so you have the knowledge to work with her, taking baby steps.
Have a read of the book I recommended. It has some useful insights.