11yr old DD with very similar probs.
she has dyslexia, dyscalculia, CAPD & ADD, and whilst i try to keep my patience with her, have found the hormones in us both raging at mo so have been picking on her a bit about stupid things like remembering stuff especially little jobs i've asked her to do to help.
This too results in her saying she's stupid, thick, dumb which then goes on to the no friends & hates herself.
She too was bullied and because of that and the education issues, i pulled her out of a large primary (60 kids in 1 school year) and put her in a class of 20 kids in school yrs 4-6. whilst education soared, friendship did not because of there only being 2 other girls in her year!!! 1 bitchy other a follower of bitchy 1. Others are 'too young' quote.
We keep a night time diary where, if she cant speak to me face to face about something, then she writes in it and i reply for the morning. Sometimes it is discussed further sometimes left, depending on circs.
the fact that your DD talks to you about it shows that you have a close relationship keep listening and just keep praising the good stuff she does.
DD hates being different. Is your DD picked on because of the exzema? try looking on the internet for famous people who have it. she might be surprised as several actresses have it.
Also have just purchased a meditation CD from Amazon called 'self esteem affirmations' by louise L Hay. which DD plays as she goes to sleep. There has been a bit of a difference. Its supposed to help with building confidence and recognizin self worth.
you could try counselling but my DD didnt find it very useful and in fact thought the counselor was stupid for wrongly interpreting what DD said. But it does work for others just make sure you have a good councellor (mine was recommended by the school service!!!!!)
good luck