10year old pulling hair and anxiety induced cough

[MummEE2]

My DD is nearly 11 years old. Ever since she was little she has always been emotionally very sensitive.

When she was aged 8 or so I noticed some of her eyelashes missing and she admitted to me she had been pulling them out and it seems to be linked with stress at school. She said they got itchy in stressful situations and when she pulled them she felt better. I spoke to school, took her to GP (who advised she'll grow out of it and to just do fun stuff over weekends with her). She stopped pulling them.

Then in July this year she pulled half of her eyebrows off. I saw her and panicked, screamed why didn't she tell me she wanted to pull them etc. I took her to see a counsellor and she attended 4 sessions and then told me she doesn't want to go anymore as she feels counselling is not helping and I am helping more.

She has not pulled any hairs since but admits to having thoughts approximately twice a month. She's also developed this weird cough which I think could be anxiety related. GP has given her tablets for allergy for cough and it's helped a bit but she still has it. GP said her chest is clear so she shouldn't be coughing but she is. And she tells me she doesn't realise she's coughing.

I feel like a failure having raised a child with mental health issues. It's really upsetting and I don't know why she is that way. Her coughing also makes me angry as I feel why cant she just stop doing that and be a normal happy 10 year old.

Any advise would be greatly appreciated